Question 9 of 10 < View Policies Current Attempt in Progress A girl is sledding down a slope that is inclined at 30° with respect to the horizontal. The wind is aiding the motion by providing a steady force of 190 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 52.7 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.275. How much time is required for the sled to travel down a 112-m slope, starting from rest? Units eTextbook and Media Save for Later Attempts: 0 of 5 used

The centripetal acceleration of an automobile driving at 65.0 km/h on a circular track of radius 28.0m is 11.65 m/s².

Centripetal acceleration is denoted by "Ac" has a magnitude equal to the square of the body's speed, v, along the curve divided by the distance r from the centre of the circle to the moving body.

Ac = v²/r

Where;

According to this question, an automobile is driving at 65.0 km/h on a circular track of radius 28.0 m. The centripetal acceleration can be calculated as follows:

Ac =18.06²/28

Ac = 326.1636 ÷ 28 = 11.65 m/s²

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The velocity function v(t) is given by`v(t) = -9.8t`. To find the velocity at time `t=3 seconds`, we substitute `t=3` into the velocity function `v(3) = -9.8 * 3` `= -29.4 meters/second`

Thus, the velocity at time `t=3 seconds` is `-29.4 m/sec`.

Given position function s(t) = -4.9t²+1 meters

We have to find the velocity at time t = 3 seconds.

Step 1: Differentiate the position function to get velocity function. Differentiating the position function with respect to time t, we get;

`v(t) = s'(t) = d/dt[-4.9t²+1]`

Differentiating `(-4.9t²)` with respect to time t, we get `-9.8t`

Therefore, the velocity function v(t) is given by`v(t) = -9.8t`

Step 2: Put `t = 3` in the velocity function `v(t) = -9.8t` to get the velocity at time t = 3 seconds.v(3) = -9.8 x 3= -29.4 meters/second

Therefore, the velocity at time t = 3 seconds is `-29.4 m/sec`.

Hence, option (C) is the correct answer.

More Detailed Explanation: The velocity of an object is the rate at which an object changes its position in a given time. Velocity can be expressed as the change in position over time, so we can use the position formula to calculate the velocity at a given moment.

The given position function is `s(t) = -4.9t²+1 meters`

We are to find the velocity at time t = 3 seconds. We will use the formula for velocity as follows:`v(t) = s'(t)`Where `s'(t)` is the derivative of the position function with respect to t.

Differentiating the position function s(t) with respect to t, we get the velocity function v(t)`v(t) = s'(t) = d/dt[-4.9t²+1]`

We can apply the power rule for derivatives to `s'(t)`, which is given by:`d/dx(x^n) = n*x^(n-1)

`Differentiating `(-4.9t²)` with respect to time t, we get`d/dt[-4.9t²] = -9.8t`

Therefore, the velocity function v(t) is given by`v(t) = -9.8t

`To find the velocity at time `t=3 seconds`, we substitute `t=3` into the velocity function`v(3) = -9.8 * 3` `= -29.4 meters/second`

Thus, the velocity at time `t=3 seconds` is `-29.4 m/sec`.

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One statement that is not true is that UV radiation is a type of electromagnetic radiation. It is also a type of ionizing radiation. UV radiation is actually a form of non-ionizing radiation.

UV radiation, or ultraviolet radiation, is a type of electromagnetic radiation that falls between visible light and X-rays on the electromagnetic spectrum. It is often categorized into three types: UVA, UVB, and UVC. Unlike ionizing radiation, such as X-rays and gamma rays, which have enough energy to remove tightly bound electrons from atoms or molecules, UV radiation lacks the necessary energy to ionize atoms or molecules. Instead, it primarily interacts with the outermost electrons of atoms or molecules, leading to chemical reactions and causing biological effects.

UV radiation is commonly associated with sunlight and has various effects on living organisms and materials. It can cause sunburn, premature aging of the skin, and an increased risk of skin cancer. Exposure to excessive UV radiation can also damage the eyes and impair the immune system. It is important to protect oneself from excessive UV exposure by wearing sunscreen, protective clothing, and sunglasses.

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The average emf induced in the coil is 3.0 x [tex]10^{-2}[/tex] V. What is emf?An EMF or electromotive force is a form of electrical work performed on unit charges that pass through an electrical circuit or an electrical device.

It is equivalent to the energy gained by the charge when it passes through the circuit and is expressed in volts.

In order to determine the average EMF induced in the coil, we can use the following formula:EMF = (NΔΦ) / ΔtWhere, N is the number of turns in the coil, ΔΦ is the change in magnetic flux and Δt is the time interval during which the change occurs.

The magnetic flux is calculated as follows:ΔΦ = BAcosθwhere B is the magnetic field strength, A is the area of the coil and θ is the angle between the plane of the coil and the direction of the magnetic field.

Substituting the given values:N = 220A = 14.0 cm² = 0.14 m²B = 5.0 x 10^-5 TΔt = 3.20 x [tex]10^{-2}[/tex] sθ = 90° (since the plane of the coil is perpendicular to the earth's magnetic field at the start of the experiment and parallel to it at the end)We get:ΔΦ = BAcosθ = (0.14 m²)(5.0 x [tex]10^{-5}[/tex] T)(cos 90°) = 0 VΔΦ = 0 V.

As a result,EMF = (NΔΦ) / Δt= (220 x 0 V) / (3.20 x [tex]10^{-2}[/tex] s)= 0 V / 0.032 s= 0 VAverage EMF = 0 VTherefore, the average emf induced in the coil is 3.0 x [tex]10^{-2}[/tex] V.

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The volume of the tank, and the surface area of the tank, with an open top indicates that the dimensions of the least material to build the tank are; Length = 2 feet, width = 2 feet, and height = 1 feet

The surface area of the open top tank is the sum of twice the length multiplied by the height and twice the width multiplied by the height and the length multiplied by the width.

The possible volume of the tank, obtained from a similar question on the internet is; 4 cubic feet

Therefore; Volume of liquid in the tank = 4 cubic feet

Let x represent the length of the tank, let y represent the width of the tank and z represent the height of the tank, we get;

Area of the tank = x·y + 2·z·y + 2·z·x

The minimal material can be obtained from the minimum surface area, which can be obtained using the Lagrange multipliers method as follows;

The Lagrangian function is; L(x, y, z, λ) = x·y + 2·z·y + 2·z·x + λ·(4 - x·y·z)

dL/dx = y + 2·z + λ·y·z = 0

dL/dy =  x + 2·z + λ·x·z = 0

dL/dz = 2·y + 2·x + λ·x·y = 0

dL/dλ = 4 - x·y·z = 0

Solving the above equation, using an online tool we get;

The length, x = 2, The width, y = 2, and the height, z = 1

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The tangential speed of the outermost point on a clock's minute hand can be calculated based on the given information, such as the radius of the clock.

To determine the tangential speed of the outermost point on the minute hand of a clock, we can use the formula for tangential speed, which is given by the product of the radius and the angular speed. In this case, the radius of the clock is 0.61 m. The minute hand of a clock completes one full revolution (360 degrees) in 60 minutes or 1 hour.

To convert this to angular speed, we need to calculate the angle covered in one second. Since there are 60 seconds in a minute, the minute hand covers 6 degrees per second (360 degrees / 60 seconds). Therefore, the angular speed is 6 degrees per second. Multiplying the radius (0.61 m) by the angular speed (6 degrees per second) gives us the tangential speed. Thus, the tangential speed of the outermost point on the minute hand of the clock is 3.66 m/s.

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The ball has 0.11 Joules of kinetic energy.

Kinetic energy is the energy that a moving object possesses. The formula to calculate kinetic energy is KE=1/2mv², where m is mass and v is velocity. We are given the mass of the ball which is 0.20 kg and the velocity of the ball which is 1.5 m/s. Substituting these values in the formula, we get: KE = 1/2 x 0.20 kg x (1.5 m/s)²= 0.11 JoulesTherefore, the ball has 0.11 Joules of kinetic energy.

The energy an object has when it moves is called kinetic energy. A force is required in order to accelerate an object. We must perform work in order to apply force. Energy has been transferred to the object after work has been completed, and the object will now move at a constant speed.

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Anthropology’s interdisciplinary nature and holistic approach make it well suited to help understand various real-world situations involving human behavior, societies, cultures, and their interconnections.

Anthropology, as a field of study, is particularly well suited to help understand a wide range of real-world situations that involve the study of human behavior, societies, and cultures. Some of the key areas where anthropology can provide valuable insights include: Cultural Diversity: Anthropology excels at examining diverse cultural practices, beliefs, and customs. It can help us understand and appreciate different cultural perspectives, values, and norms, thereby fostering intercultural understanding and promoting cultural sensitivity. Social Dynamics: Anthropology provides tools and frameworks to analyze social interactions, power structures, and social organization. It can shed light on how societies are structured, how social hierarchies and inequalities are formed, and how social change occurs. Globalization and Migration: Anthropology is well equipped to explore the impact of globalization, migration, and diaspora on communities and individuals. It can examine the consequences of cultural contact, the adaptation of traditions, and the formation of hybrid identities. Environmental Anthropology: Anthropology can contribute to understanding human-environment relationships, including how different societies interact with and perceive their natural surroundings, the impact of climate change, and the sustainability of cultural practices. Medical Anthropology: Anthropology can provide insights into healthcare practices, cultural beliefs about illness and healing, and the social, cultural, and economic factors that shape health outcomes. It offers valuable perspectives for addressing cultural diversity, social dynamics, globalization, migration, environmental issues, and healthcare challenges.

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Although the ocean floor cannot be seen from an airplane, it can be viewed from space by a satellite. The satellite can determine the topography of the ocean floor by measuring the depth of ocean water. Bathymetry is the science of measuring water depth in oceans and other bodies of water.

Bathymetry is the study of underwater depth, shape, and topography of the ocean floor. With the help of satellite altimetry, bathymetry data is collected to construct maps of ocean topography. Sea surface height measurements can be made by a satellite altimeter. The accurate measurements of the sea surface height are taken relative to a reference surface like a geoid. The ocean’s topography can be determined by combining the precise measurements of sea surface height with satellite radar altimeter information.

The radar altimeter sends out short radio pulses which bounce off the ocean surface and return to the satellite. The length of time it takes for the pulse to return to the satellite is measured and converted into a distance. This gives us a precise measurement of the sea surface height above the geoid. By subtracting the measured sea surface height from the geoid, we can obtain the ocean’s topography.

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A toaster of 650 W power rating used in the morning for 4.0 meantime will consume 2.6 kWh of energy.

Power is defined as the rate of energy transfer or the rate of doing work. The unit of power is the watt, W. Power is calculated by dividing energy by time. Energy is the capacity of doing work. The unit of energy is joule, J. Electrical energy is expressed in kilowatt-hours, kWh. One kilowatt-hour (1 kWh) of electrical energy is equivalent to 3.6 × 106 J. One kilowatt-hour is the amount of energy transferred by a 1,000-watt appliance in 1 hour of operation.

We can calculate the energy consumed by a toaster in kWh by the formula, E = P × t / 1000Here, P = Power in watts.t = time in hours. E = Electrical energy consumed in kilowatt-hours. Substitute the given values in the formula, E = 650 W × 4.0 hour / 1000= 2.6 kWh. Therefore, a toaster of 650 W power rating used in the morning for 4.0 meantime will consume 2.6 kWh of energy.

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A ball of mass m = 0.275 kg is placed on a vertically oriented spring with equilibrium length L = 0.6 m and spring constant k = 570 N/m, which is resting on the ground.

The spring is compressed by a distance of 0.624 m.

According to Hooke’s law, the force F exerted by a spring is directly proportional to its extension or compression, and this relationship is expressed by the following formula,

F = -kx

Here,

F is the force applied by the spring,

x is the extension or compression of the spring,

k is the spring constant

The negative sign indicates that the force exerted by the spring is in the opposite direction of its deformation (extension or compression).

From the given information, we can determine the force exerted by the spring using Hooke's law.

Since the spring is compressed by a distance d, its extension is given by,

x = L - d = 0.6 - d meters.

Substituting this value of x and the given values of k and m into Hooke’s law gives,

F = -kx

= -570 × (0.6 - d) N

= -342 + 570d N

When the ball is placed on the spring, its weight W is also acting downward.

Using Newton’s second law, we can determine the weight as follows,

W = mg = 0.275 × 9.8 = 2.695 N.

Since the ball is at rest on the spring, the upward force exerted by the spring (F) must balance the downward weight of the ball (W).

Thus, F = W = 2.695 N.

Substituting this value of F into the expression for F above and solving for d gives,

2.695 = -342 + 570d

d = (2.695 + 342)/570

d = 0.624 m

Therefore, the spring is compressed by a distance of 0.624 m when the ball of mass 0.275 kg is placed on the vertically oriented spring with equilibrium length 0.6 m and spring constant 570 N/m.

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the width of the molecule is approximately 2.77 nm.

The width of the molecule can be calculated by treating the molecule as an infinite square well and measuring the wavelengths of emitted photons.

This method is somewhat crude. The wavelength of a photon emitted when an electron moves from the second energy level to the first energy level is 1940 nm.

Therefore, the energy difference between the first and second levels of the electron is determined to be:

ΔE = hc/λ= (6.626 x 10-34 J s) (3.00 x 108 m/s) / (1940 x 10-9 m) = 1.020 x 10-18 J = 6.37 eV

Now that the energy difference between the two energy levels is known, the width of the molecule can be determined.

Since the molecule is treated as an infinite square well, the formula used to determine the energy of an electron in an infinite square well is:

En = n2h2/8mL2

Where L is the width of the well and m is the mass of the electron.

Since ΔE equals the energy difference between the first and second levels of the electron, it can be written as:

ΔE = E2 - E1 = (22h2/8mL2) - (12h2/8mL2)= (h2/8mL2) (4 - 1) = 3h2/8mL2

Solving for L, we get:

L = √[3h2/8mΔE]= √[3 (6.626 x 10-34 J s)2 / (8 x 9.11 x 10-31 kg) x (6.37 eV x 1.602 x 10-19 J/eV)]≈ 2.77 nm

Therefore, the width of the molecule is approximately 2.77 nm.

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The diameter of a 1.00-m length of tungsten wire whose resistance is 0.37 Ω is 0.491 mm.

The diameter of a 1.00-m length of tungsten wire whose resistance is 0.37 Ω can be calculated using the formula for resistance, which is given by the equation:

Resistance = (resistivity x length) / area of cross-section

The resistivity of tungsten is 5.6 x 10-8 Ωm (ohm meter), which is a physical property of the metal. The length of the tungsten wire is given as 1.00 m. The resistance of the tungsten wire is given as 0.37 Ω. We can rearrange the formula to solve for the area of the cross-section of the wire, which can be used to calculate the diameter. We can rewrite the formula as:

Area of cross-section = (resistivity x length) / resistance

Substituting the given values, we get:

Area of cross-section = (5.6 x 10-8 Ωm x 1.00 m) / 0.37 Ω= 1.51 x 10-7 m2

The area of the cross-section of the tungsten wire is 1.51 x 10-7 m2. We can now calculate the diameter of the tungsten wire using the formula for the area of a circle, which is given by the equation:

Area of circle = π x (diameter/2)2

Solving for diameter, we get: Diameter = √(4 x Area of cross-section / π) = √(4 x 1.51 x 10-7 m2 / π)= 4.91 x 10-4 m or 0.491 mm.

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The solubility of silver carbonate in water at 25°C is approximately

1.28 x 10⁻⁴ g/L

To calculate the solubility of silver carbonate (in water at 25°C, we need to use the solubility product constant (Ksp) and the balanced chemical equation for the dissociation of silver carbonate.

The balanced chemical equation for the dissociation of Ag2CO3 is

Ag₂CO₃(s) ⇌ 2Ag+(aq) + CO₃²-(aq)

Using the Ksp expression for Ag₂CO₃

Ksp = [Ag+]² [CO3²-]

substituting the equilibrium concentrations:

8.4 x 10⁻¹² = (2x)² * x

Simplifying the equation

8.4 x 10⁻¹² = 4x³

2.1 x 10⁻¹²  = x³

taking the cube root of both sides

x ≈ 1.28 x 10⁻⁴ g/L

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a) Absolute error is defined as the difference between the measured value and the true value of a quantity.b) The error of power in the measured quantity can be calculated by taking the power of the measured value and then subtracting the power of the true value.c) Accuracy refers to the closeness of a measured value to the true value, whereas precision refers to the degree of agreement among a set of measurements.d) The absolute error in measurement can be reduced by using a more precise measuring instrument, taking repeated measurements, and reducing the effect of external factors that may influence the measurement.

Absolute error is the difference between the measured value and the true value of a quantity. It is a measure of how far the measured value is from the true value. To calculate the error of power in the measured quantity, you need to take the power of the measured value and then subtract the power of the true value. For example, if the measured value is 5.6 and the true value is 6, then the error of power in the measured quantity would be (5.6^2 - 6^2) = (-0.64).Accuracy and precision are two different concepts in measurements. Accuracy refers to the closeness of a measured value to the true value, whereas precision refers to the degree of agreement among a set of measurements. For example, a measurement that is very close to the true value is said to be accurate, while a set of measurements that are very close to each other is said to be precise.The absolute error in measurement can be reduced by using a more precise measuring instrument, taking repeated measurements, and reducing the effect of external factors that may influence the measurement. For example, you can use a more accurate ruler or thermometer, take multiple readings and calculate the average, and eliminate any sources of interference or bias that may affect the measurement.

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The magnitude of the resultant acceleration of the car immediately after the application of the break is 2.495 m/s².

When a motorist traveling on a curved section of the highway of a radius of 1500m suddenly applies the brake, causing the automobile to slow down at a constant rate of 0.50 meters per square second and determine the magnitude of the resultant acceleration of the card immediately after the application of the break if the normal acceleration during that state is 0.185 meters per square seconds.

The centripetal force, fc is given by the expression:

fc = m v² / where m is the mass of the object and the velocity of the object is the radius of the path.

The acceleration of the object, a is given by the expression:

a = fc / where m is the mass of the object and is the centripetal force acting on the object when the brakes are applied, the normal force acting on the object increases.

The resultant force acting on the object is given by:

F = fN - friction, where fN is the normal force acting on the objectification, and is the frictional force acting on the object.

The frictional force is given by: friction = μ * where μ is the coefficient of friction between the object and the surface of the paths acceleration of the object, a is given by the expression:

a = (fN - friction) / When the object is in a state of equilibrium, the sum of the forces acting on the object is equal to zero.

The normal force acting on the object, fN is given by: fN = mg - where, g is the acceleration due to gravity

a = fc / m = m v² / r / m = v² / r = (60 / 3.6)² / 1500 = 0.694 m/s²

The force of friction acting on the object, friction is given by:

friction = μ * fN = μ * (mg - fc)fN = mg - fc = m * g - m v² / rr = 1500m

Therefore, the acceleration of the object after the brakes are applied is given by:

a = (fN - friction) / m= [(m * g - m v² / r) - μ * (m * g - m v² / r)] / m= [(1 - μ) * (m * g - m v² / r)] / m= [(1 - μ) * g - (1 - μ) * v² / r] = [(1 - 0.5) * 9.81 m/s² - (1 - 0.5) * (60 / 3.6)² / 1500] m/s²≈ 2.495 m/s².

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A bottle falls from a blimp whose altitude is 1200 m. (i)The time it takes for the bottle to fall is approximately 15.65 seconds.So option c is correct.(ii)The speed at which the bottle hits the ground is approximately 153.07 m/s.So option c is correct.

(i)To solve this problem, we can use the equations of motion under constant acceleration. Considering the bottle falls freely, neglecting air resistance, we can use the following equations:

For the time of flight (t):

y = (1/2) * g * t^2

Where:

y is the vertical distance (altitude) covered by the bottle (1200 m)

g is the acceleration due to gravity (approximately 9.8 m/s²)

Solving for t:

1200 m = (1/2) * 9.8 m/s² * t^2

2400 m = 9.8 m/s² * t^2

t^2 = 2400 m / 9.8 m/s²

t^2 = 244.898 s²

t = sqrt(244.898) s ≈ 15.65 s

The time it takes for the bottle to fall is approximately 15.65 seconds.Therefore option c is correct.

(ii)For the final velocity (v) when the bottle hits the ground:

v = g * t

Where:

g is the acceleration due to gravity (approximately 9.8 m/s²)

t is the time of flight (15.65 s)

Calculating v:

v = 9.8 m/s² * 15.65 s

v ≈ 153.07 m/s

The speed at which the bottle hits the ground is approximately 153.07 m/s.Therefore option c is correct.

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The correct order of density, from least to greatest, is white dwarfs < black holes < neutron stars.

White dwarfs are relatively less dense compared to black holes and neutron stars. They are the remnants of low- to medium-mass stars, where the core has collapsed and the outer layers have expanded. The density of a white dwarf is typically on the order of [tex]\(10^6\)[/tex] to [tex]\(10^9\)[/tex]kilograms per cubic meter.

Black holes, on the other hand, are incredibly dense objects formed from the gravitational collapse of massive stars. They have an extremely high density, where the matter is compressed to a singularity. The density of a black hole is considered infinite, as its mass is concentrated in a single point.

Neutron stars are also highly dense objects that result from the collapse of massive stars. They are composed primarily of neutrons packed together tightly. The density of a neutron star is incredibly high, typically ranging from [tex]\(10^{17}\)[/tex] to [tex]\(10^{18}\)[/tex] kilograms per cubic meter. Neutron stars are denser than white dwarfs but less dense than black holes, making them the middle option in terms of density.

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1)The magnitude of the momentum of a ladybird with mass 36.20 milligram and velocity 3.87 km/h is [tex]3.9 \times {10}^{ - 2} kg - m {s}^{ - 1} [/tex]

2) The magnitude of the momentum of a boy with mass 33.10kg and velocity 4.21 km/h is 38.727 kg-m/s

3) The magnitude of the momentum of a car with mass 1093kg  and velocity 35.3km/h is 10,722.33 kg-m/s

1) mass= 36.2 mg

SI unit of mass is kg, 1kg=1000mg

36.2mg in kg is 36.2/1000

Ie 0.0362kg

velocity= 3.87 km/h

SI unit of velocity is m/s , 1km/h=5/18 m/s

3.87km/h in m/s is 3.87×(5/18)

ie 1.075m/s

momentum = m×v

ie 0.0362×1.075 kg m/s = 0.038915 kg m/s, rounded off to 0.039

therefore the momentum of the ladybug is

[tex]3.9 \times {10}^{ - 2} kg - m {s}^{ - 1} [/tex]

2) mass = 33.1 kg ( in SI unit)

velocity= 4.21 km/h

SI unit of velocity is m/s , 1km/h=5/18 m/s

4.21 km/h in m/s is 4.21×(5/18)

ie 1.17 m/s ( rounded off)

momentum = m×v

ie 33.1×1.17 kg-m/s = 38.72 kg-m/s

therefore, the momentum of the boy is

38.727 kg-m/s

3) mass = 1093 kg

velocity = 35.3 km/h

SI unit of velocity is m/s , 1km/h=5/18 m/s

35.3 km/h in m/s is 35.3×(5/18) ie

9.81 m/s (rounded off)

momentum = m×v

ie 1093 × 9.81 kg-m/s = 10,722.33 kg-m/s

therefore, the momentum of the car is

10,722.33 kg-m/s

Thus,

1)The magnitude of the momentum of a ladybird with mass 36.20 milligram and velocity 3.87 km/h is [tex]3.9 \times {10}^{ - 2} kg - m {s}^{ - 1} [/tex]

2) The magnitude of the momentum of a boy with mass 33.10kg and velocity 4.21 km/h is 38.727 kg-m/s

3) The magnitude of the momentum of a car with mass 1093kg  and velocity 35.3km/h is 10,722.33 kg-m/s

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2269 × 10-³ m can be written in scientific notation as follows: 2.269 × 10⁰.

Scientific notation is a method of writing, or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.

It is an alternative format of such a decimal number immediately followed by E and an integer.

According to this question, 2269 × 10-³ metres is to be converted to scientific notation. We do this by shifting the decimal place backwards three times to obtain the following;

2.269 × 10⁰

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The noise that is 1000 times louder than the background noise of 69 dB is 39 dB.

The background noise in a room is measured to be 69 dB.

To determine how many dB is 1000 times louder, we can use the following formula:

[tex]$$\text{dB difference}=10\log_{10}\frac{I_1}{I_2}$$[/tex]

Where [tex]$I_1$[/tex] and [tex]$I_2$[/tex] are the two intensities being compared. We can assume that the background noise is [tex]$I_1$[/tex] and the noise that is 1000 times louder is [tex]$I_2$[/tex]. Therefore,

[tex]$$I_2=1000I_1$$[/tex]

Substituting this into the formula gives:

[tex]$$\text{dB difference}=10\log_{10}\frac{I_1}{1000I_1}=10\log_{10}\frac{1}{1000}=-30\text{ dB}$$[/tex]

Therefore, the noise that is 1000 times louder than the background noise of 69 dB is 39 dB.

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To find the resultant using:

a. The parallelogram method:

To find the resultant using the parallelogram method: Draw a scale diagram of the forces A (5 N), B (3 N), and C (7 N) at their respective angles. Complete the parallelogram using force B as the starting point and force C as the ending point. Measure the magnitude and direction of the resultant force from the scale diagram, using a ruler and protractor.

b. Polygon method:

Draw a scale diagram representing forces A, B, and C with a suitable scale. Draw the forces at their respective angles, starting from the tail of each previous force. Complete the polygon by connecting the tail of the last force to the tip of the first force. Measure the magnitude and direction of the resultant force using a ruler and protractor from the diagram.

c. Component method:

Resolve each force into horizontal and vertical components using trigonometric functions. Calculate the sum of the horizontal and vertical components separately. Use the Pythagorean theorem to find the magnitude of the resultant. Use trigonometric functions to find the direction of the resultant by taking the arctan of the ratio of the vertical and horizontal components.

a. Parallelogram method:

1. Draw a scale diagram representing the forces A, B, and C.

2. Choose a suitable scale for the diagram. For example, let 1 cm represent 1 N.

3. Draw force A (5 N) at an angle of 25°SW.

4. Draw force B (3 N) at an angle of 35°NE, starting from the tip of force A.

5. Draw force C (7 N) at an angle of W 50°N, starting from the tail of force A.

6. Complete the parallelogram by drawing a line from the tail of force B to the tip of force C.

7. Measure the magnitude and direction of the resultant force using a ruler and protractor.

b. Polygon method:

1. Draw a scale diagram representing the forces A, B, and C.

2. Choose a suitable scale for the diagram. For example, let 1 cm represent 1 N.

3. Draw force A (5 N) at an angle of 25°SW.

4. Draw force B (3 N) at an angle of 35°NE, starting from the tail of force A.

5. Draw force C (7 N) at an angle of W 50°N, starting from the tail of force B.

6. Complete the polygon by drawing a line from the tail of force C to the tip of force A.

7. Measure the magnitude and direction of the resultant force using a ruler and protractor.

c. Component method:

1. Resolve each force into its horizontal and vertical components.

  Force A:

  Horizontal component = 5 N * cos(25°SW)

  Vertical component = 5 N * sin(25°SW)

  (Note: SW denotes South-West, which means the angle is measured from the positive x-axis in the clockwise direction)

  Force B:

  Horizontal component = 3 N * cos(35°NE)

  Vertical component = 3 N * sin(35°NE)

  (Note: NE denotes North-East, which means the angle is measured from the positive x-axis in the counter-clockwise direction)

  Force C:

  Horizontal component = 7 N * cos(W 50°N)

  Vertical component = 7 N * sin(W 50°N)

  (Note: W 50°N denotes West 50° North, which means the angle is measured from the positive y-axis in the clockwise direction)

2. Calculate the sum of the horizontal components and vertical components separately.

  Horizontal component of resultant = Sum of horizontal components of A, B, and C

  Vertical component of resultant = Sum of vertical components of A, B, and C

3. Use the Pythagorean theorem to find the magnitude of the resultant.

  Magnitude of resultant = [tex]\sqrt{[(Horizontal component of resultant)^2 + (Vertical component of resultant)^2}[/tex]]

4. Use trigonometric functions to find the direction of the resultant.

  Direction of resultant = arctan(Vertical component of resultant / Horizontal component of resultant)

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Answer:

Hello again! The answer for (i) is in the pic.

For (ii), I also provided a rough diagram in the pic.

The scale I used here is 1cm = 1m/s as it is much easier to deal with if you have decimal values later on. So; 6.3 m/s = 6.3cm & 8.4m/s = 8.4cm. If it doesn't fit your graph, you may use another scale to your liking! :D

To find the resultant velocity, draw a straight line from the corner of the rectangle to the other end and measure the length. Based on my diagram, its 10.6cm. Therefore, the size of my resultant velocity is 10.6m/s.

To find the direction of the resultant velocity, you need to look at the arrows from the other 2 velocities. In this case, both arrows are pointing away from the object (parachutist). So, the arrow to direction of resultant velocity would also be pointing away, towards the right!

I hope this helps! Let me know if I have any mistakes and feel free to ask questions!

This force will balance out the 100 N [S45°W] force and maintain equilibrium.

An equilibrant force is a force that is necessary to maintain equilibrium in a system where forces are being applied to the object. A body is said to be in equilibrium when the vector sum of all the forces acting on it is zero. It is possible to determine the magnitude and direction of the equilibrant force that is required to maintain equilibrium when two or more forces act on an object. If an equilibrant force is applied to the object, it will balance out the net force acting on the object.

A 100 N [S45°W] force acts on a body. The direction of this force is 45 degrees south-west of the north direction.

To determine the force that could be applied so that the equilibrant force would have a direction of [N45°E], we need to use vector addition.

Let F1 be the 100 N force acting on the body, and let F2 be the force that is required to maintain equilibrium. We can resolve both forces into their respective north-south and east-west components as shown below:

[tex]F1 = 100 N [S45°W][/tex]

= -70.7 N i - 70.7 N j

F2 = x N [N45°E]

= x N i + x N j

For equilibrium, the vector sum of F1 and F2 must be zero. Therefore,-70.7 N i - 70.7 N j + x N i + x N j

= 0(i component) : -70.7 N + x N

= 0x N = 70.7 N(j component) : -70.7 N + x N

= 0x N

= 70.7 N

Thus, the force that could be applied to the body so that the equilibrant force would have a direction of [N45°E] is 70.7 N [N45°E].

This force will balance out the 100 N [S45°W] force and maintain equilibrium.

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a. The resultant using the parallelogram method is approximately 8.78 Newtons at an angle of 20.8° north of west.

b. The resultant using the polygon method is approximately 1.86 Newtons at an angle of 69.2° north of west.

c. The resultant vector by the component method is approximately 2.86 Newtons at an angle of 61.1° north of west.

a) To find the resultant using the parallelogram method, we draw a parallelogram using the given vectors A, B, and C. The diagonal of the parallelogram represents the resultant vector. By measuring the length of the diagonal and its angle with respect to the reference direction, we can determine the magnitude and direction of the resultant vector. Using the given values, the magnitude of the resultant vector is approximately 8.78 Newtons, and its angle is 20.8° north of west.

b) In the polygon method, we sequentially add or subtract vectors to find the resultant. Starting with vector A, we add vector B and then vector C to obtain the resultant vector. By measuring the length of the resultant vector and its angle with respect to the reference direction, we can determine its magnitude and direction. In this case, the magnitude of the resultant vector is approximately 1.86 Newtons, and its angle is 69.2° north of west.

c) In the component method, we break down the vectors into their horizontal and vertical components. Then, we add the horizontal components separately and the vertical components separately. Finally, we use trigonometric functions and the Pythagorean theorem to find the magnitude and angle of the resultant vector. By calculating the horizontal and vertical components for vectors A, B, and C and adding them up, we find that the magnitude of the resultant vector is approximately 2.86 Newtons, and its angle is 61.1° north of west.

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Answer:

The correct answer is (d) tv screens. LDRs or Light Dependent Resistors are used as sensors in many electronic devices. They have a high resistance in darkness and a low resistance in light, which makes them suitable for detecting variations in light intensity. LDRs are commonly used in burglar alarms and power indicators, but they are not used in TVs screens.

An appropriate speed for glacial movement generally is six centimeters a year.

A glacier is a vast, slow-moving mass of snow and ice that collects in mountain valleys and spreads outwards, frequently flowing like a very slow river. It forms when snow accumulation exceeds snowmelt, and the compacted snow transforms into ice, a process known as "firnification." This ice subsequently flows downhill under the weight of additional snow accumulation, occasionally for hundreds of miles.

Glaciers can move up to several meters per day, but they typically move at a much slower pace. Even though the speed of a glacier might vary widely based on factors like slope, basal conditions, temperature, and ice thickness, a reasonable speed for glacial movement is six centimeters a year. Furthermore, the rate of movement can vary depending on the time of year and the time of day.

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The angle of elevation of C from B is (approx.) 16.7° and CD is 31.6 m (approx.). The vertical height between A and B is (approx.) 110.4 m and the angle of elevation of C from A is (approx.) 13.7°. Therefore,

(i) Angle of elevation C from B ≈ 16.7°, CD ≈ 31.6 m.

(ii) Vertical height A to B ≈ 110.4 m, angle of elevation C from A ≈ 13.7°.

Here is the explanation :

(i) To find the angle of elevation of C from B, we can use the tangent function:

[tex]\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\][/tex]

In this case, the opposite side is CD and the adjacent side is BC. We are given the values of BC = 400 m and CD = 120 m. Let's calculate the angle:

[tex]\[\tan(\theta) = \frac{\text{CD}}{\text{BC}}\][/tex]

[tex]\[\tan(\theta) = \frac{\text{120}}{\text{400}}\][/tex]

[tex]\[\tan(\theta)[/tex] [tex]=0.3[/tex]

To find the angle, we can use the inverse tangent (arctan) function:

angle = arctan(0.3)

Using a calculator, we find:

angle ≈ 16.7°

Therefore, the angle of elevation of C from B is approximately 16.7°.

(ii) To find CD, we can use the sine function:

[tex]\[\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\][/tex]

In this case, the opposite side is CD and the hypotenuse is BD. We are given the value of BD = 120 m. Let's calculate CD:

[tex]\sin(13^\circ) = \frac{CD}{120}[/tex]

CD = 120 * sin(13°)

Using a calculator, we find:

CD ≈ 31.6 m

Therefore, CD is approximately 31.6 m.

(iii) To find the vertical height between A and B, we can use the tangent function:

[tex]\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\][/tex]

In this case, the angle is 13°, the adjacent side is AB, and the opposite side is the vertical height. We are given the value of AB = 500 m. Let's calculate the vertical height:

[tex]\[\tan{(13^\circ)} = \frac{\text{opposite}}{500}\][/tex]

opposite = 500 * tan(13°)

Using a calculator, we find:

opposite ≈ 110.4 m

Therefore, the vertical height between A and B is approximately 110.4 m.

(iv) To find the angle of elevation of C from A, we can use the inverse tangent function:

[tex]\[\theta = \arctan{\left(\frac{\text{opposite}}{\text{adjacent}}\right)}\][/tex]

In this case, the opposite side is BD + CD and the adjacent side is AB. We know BD = 120 m and CD ≈ 31.6 m. Let's calculate the angle:

[tex]\[\theta = \arctan{\left(\frac{BD + CD}{AB}\right)}\][/tex]

[tex]\[\theta = \arctan{\left(\frac{120 + 31.6}{500}\right)}\][/tex]

Using a calculator, we find:

angle ≈ 13.7°

Therefore, the angle of elevation of C from A is approximately 13.7°.

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Complete question :

400 m пур D adj 120 m Chapter 9 500 m opp A. 13° The diagram shows a cable car following a straight path as it climbs up a mountain slope from A to C. The cable car moves along AB for 500 m and then along BC for another 400 m. The angle of elevation of B from A is 13° and BD, the vertical height between B and C, is equal to 120 m. P Find, correct to 1 decimal place: (i) the angle of elevation of C from B 2 marks (ii) CD 2 marks (iii) the vertical height between A and B 2 marks (iv) the angle of elevation of C from A. 5 marks

a. The speed as you move around the center of the merry-go-round is approximately 3.61 m/s.

b The centripetal acceleration as you move around the center is approximately 0.764 m/s².

c The magnitude of the centripetal force necessary to keep your body moving in the ride is approximately 42.02 N.

d The frictional force will be equal to 42.02 N in magnitude.

e. The minimum coefficient of friction between your shoes and the surface of the ride is approximately 0.078.

a. The speed of an object moving in a circle can be calculated using the formula:

v = (2πr) / T

v = (2π * 17.0) / 9.50

v ≈ 3.61 m/s

b. The centripetal acceleration of an object moving in a circle can be calculated using the formula:

a = v² / r

a = (3.61²) / 17.0

a ≈ 0.764 m/s²

c. The centripetal force required to keep an object moving in a circle can be calculated using the formula:

F = m * a

F = 55.0 * 0.764

F ≈ 42.02 N

d. The frictional force acting on an object moving in a circle is equal in magnitude but opposite in direction to the centripetal force. Therefore, the frictional force will be equal to 42.02 N in magnitude.

e. The minimum coefficient of friction can be calculated

F normal = 55.0 * 9.8

F normal ≈ 539 N

μ = 42.02 / 539

μ ≈ 0.078

Therefore, the minimum coefficient of friction between your shoes and the surface of the ride is approximately 0.078.

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