A new planet called "Corus" was discovered by a team of astronomers that


is 60 x 106 km away from Earth. A satellite was launched by a rocket from


Earth to reach Corus. At a specific distance from Corus, the rocket releases


the satellite to the orbit of the planet. The satellite makes one complete


revolution around Corus in 15 Earth days. If Corus has a similar mass to


Mars, propose a suitable mass of the satellite and estimate:


i.


ii.


Distance between the satellite and the Corus's surface


Satellite's gravitational acceleration towards the core of Corus


Gravitational force between the satellite and the Corus


Minimum speed of the satellite to orbit Corus


iv.

The force between the two particles remains the same when both charges and the separation are doubled.

If the charge of each of the two particles is doubled and the separation between them is also doubled, the force between the two particles can be determined using Coulomb's Law:

F = (k * |q1 * q2|) / r^2

When both charges (q1 and q2) are doubled, the numerator becomes 4 * |q1 * q2|. And when the separation (r) is doubled, the denominator becomes (2r)^2 = 4r^2.

So, the new force (F') is:

F' = (k * 4|q1 * q2|) / (4r^2)

By canceling out the "4" in both numerator and denominator:

F' = (k * |q1 * q2|) / r^2

You'll notice that F' = F, which means the force between the two particles remains the same when both charges and the separation are doubled.

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The man hikes 6.6 km north with an average velocity of 4.2 km/h to the north. We can use the equation:

distance = velocity x time

to find the time it takes for him to complete the first part of the hike. Solving for time, we get:

time = distance / velocity

time = 6.6 km / 4.2 km/h

time = 1.57 hours

After resting at the bench for 15 minutes (or 0.25 hours), the man continues hiking 3.8 km north with an average velocity of 5.1 km/h to the north.

Again, we can use the same equation to find the time it takes for him to complete this part of the hike:

time = distance / velocity

time = 3.8 km / 5.1 km/h

time = 0.75 hours

To find the total time for the hike, we simply add the time for the first part of the hike, the rest, and the second part of the hike:

total time = 1.57 hours + 0.25 hours + 0.75 hours

total time = 2.57 hours

So, the total hike lasts for 2.57 hours. It's important to note that we assumed the man did not take any breaks during the second part of the hike, and that he continued hiking at a constant velocity. Additionally, we assumed that the path he took was a straight line.

However, in reality, the path may not be a straight line and the man may take breaks or adjust his velocity during the hike.

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Two lines meet at a point that is also the vertex of a right angle. The value of x is 0 degrees, the value of ∠CAE is 0 degrees and the value of ∠BAG is 90 degrees.

Since the point of intersection is the vertex of a right angle, we know that the sum of the angles formed by the two lines must be 180 degrees.

Let's assume that angle BAC is equal to x. Then we have:

∠BAC + ∠CAD + ∠BAE = 180 degrees

Since ∠CAD and ∠BAE are both right angles, we have:

x + 90 degrees + 90 degrees = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 90 degrees - 90 degrees

x = 0 degrees

Therefore, angle BAC is equal to 0 degrees.

Since angle CAD is a right angle, angle CAE is equal to 90 degrees - angle CAD. Substituting 90 degrees for angle CAD, we get:

∠CAE = 90 degrees - 90 degrees = 0 degrees

Therefore, angle CAE is also equal to 0 degrees. Similarly, since angle BAE is a right angle, angle BAG is equal to 90 degrees - angle BAE. Substituting 90 degrees for angle BAE, we get:

∠BAG = 90 degrees - x = 90 degrees - 0 degrees = 90 degrees

Therefore, angle BAG is equal to 90 degrees.

In summary, by using the fact that the sum of the angles formed by the two lines must be 180 degrees, we can solve for the value of x and the measurements of angles CAE and BAG. We found that x is equal to 0 degrees, angle CAE is equal to 0 degrees, and angle BAG is equal to 90 degrees.

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The tension in the second rope is approximately 1937.98 N.

To find the tension in the second rope, we can start by calculating the total weight of the load. The weight (W) can be calculated using the formula:

W = mass × acceleration due to gravity
W = 478 kg × 9.8 m/s²
W = 4684.4 N

Let the tension in the second rope be T2, and the tension in the first rope is 2.2 times T2. Thus, the tension in the first rope is 2.2T2.

Since the two ropes are perpendicular to each other, we can use the Pythagorean theorem to find the resultant tension (which is equal to the weight of the load):

W² = (2.2T2)² + T2²

Substituting the value of W (4684.4 N):

(4684.4)² = (2.2T2)² + T2²

Now, we can solve for T2:

T2²(1 + 2.2²) = 4684.4²
T2²(5.84) = 21929539.36
T2² = 3755062.91
T2 = √3755062.91
T2 ≈ 1937.98 N

So, the tension in the second rope is approximately 1937.98 N.

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The resolution of a stopwatch is the smallest time interval that can be measured accurately by the device.

To determine the resolution of a stopwatch, one can look at the number of digits displayed on the stopwatch and the precision of the timing mechanism.

For example, if a stopwatch displays time in increments of 0.01 seconds, it has a resolution of 0.01 seconds or 10 milliseconds. If the stopwatch displays time in increments of 0.001 seconds, it has a resolution of 0.001 seconds or 1 millisecond.

The coach should choose a stopwatch with a resolution that is appropriate for the level of precision required for timing the ball accurately.

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The pressure exerted by the girl on the ground is (a) 33,333.33 N/m² (Pa) with high heels and (b) 12,500 N/m² (Pa) with flat soles.

To calculate the pressure exerted by the girl on the ground, we will use the formula:

Pressure (P) = Force (F) / Area (A)

Force (F) can be calculated using the formula F = mass (m) × gravitational field strength (g).

For this problem, mass (m) = 50 kg and gravitational field strength (g) = 10 N/kg.

First, let's calculate the force exerted by the girl:

F = m × g = 50 kg × 10 N/kg = 500 N

Now we will calculate the pressure exerted for both cases:

(a) High heels with an area of 150 cm²:
We need to convert the area to m², so A = 150 cm² × (1 m² / 10,000 cm²) = 0.015 m².

Pressure (P) = F / A = 500 N / 0.015 m² = 33,333.33 N/m² or Pa.

(b) Flat soles with an area of 400 cm²:
We need to convert the area to m², so A = 400 cm² × (1 m² / 10,000 cm²) = 0.04 m².

Pressure (P) = F / A = 500 N / 0.04 m² = 12,500 N/m² or Pa.

So, the pressure exerted by the girl on the ground is (a) 33,333.33 N/m² (Pa) with high heels and (b) 12,500 N/m² (Pa) with flat soles.

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Answer:

35

Explanation:

Let Angle of Incident ray be i.

Let Angle of Reflected ray be r.

By laws of reflection

i = r

Here

i + r = 70

i + i = 70

2i = 70

i = 70/2

i = 35

Hence

The angle of incidence for this ray is 35.

The wavelike nature of a moving baseball is typically not observed due to its relatively large mass and size in comparison to the extremely small scale of quantum mechanical effects, where wave-particle duality becomes significant.

Wave-particle duality is a fundamental concept in quantum mechanics, stating that particles like electrons can exhibit both particle-like and wave-like properties.

However, this behavior is most noticeable in extremely small objects, such as subatomic particles. The de Broglie wavelength is used to describe the wavelike nature of a particle and is given by the formula λ = h/(mv), where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.

For macroscopic objects like a baseball, the mass is large, making the de Broglie wavelength incredibly small. As the wavelength becomes smaller, the wavelike nature becomes less significant, and the object behaves more like a particle.

In the case of a moving baseball, the de Broglie wavelength is so small that the wavelike nature becomes essentially negligible and unobservable.

Furthermore, macroscopic objects like baseballs interact with their surroundings (e.g., air molecules) more frequently than subatomic particles.

This interaction, known as decoherence, reduces the visibility of quantum mechanical effects such as wave-particle duality.

In summary, the wavelike nature of a moving baseball is typically not observed due to its large mass and size, resulting in an extremely small de Broglie wavelength, and the frequent interaction with its surroundings, which reduces the visibility of quantum mechanical effects.

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The height of the cliff is approximately 490 meters (or about 1,607 feet).

To find the height of the cliff, we can use the kinematic equation:

[tex]h = 1/2 * g * t^2[/tex]

where h is the height of the cliff, g is the acceleration due to gravity (which is approximately 9.8 m/s²), and t is the time it takes for the rock to hit the ground.

In this case, we know that the time it takes for the rock to hit the ground is 10.0 seconds.

So we can plug in the values:

[tex]h = 1/2 * 9.8 m/s^2 * (10.0 s)^2[/tex]

h = 490 m

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When you double your height, your new potential energy is 114 Joules.

The potential energy of an object depends on its height (h) and the force of gravity acting on it (usually denoted as "g"). The formula for gravitational potential energy is given by:

P = mgh

where P is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height.

In this case, you have a potential energy of 57 J. Let's assume that the height (h) is constant, and we'll denote it as h1. So, we have:

P = mgh1 = 57 J

Now, you double your height, which means the new height is 2 times the original height (2h1). Let's denote the new height as h2. So, we have:

h2 = 2h1

Substituting this into the formula for potential energy, we get:

P = mgh2 = mg(2h1)

Since h2 = 2h1, we can rewrite the above expression as:

P = 2(mgh1)

But we know that PE1 = mgh1, so we can substitute this value into the equation:

PE2 = 2(PE1)

So, the new potential energy is:

P = 2*57J = 114J

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(a) The tension in the rope at an angle of 10° above the horizontal is approximately 798.5.4 N.

(b) The tension in the rope at an angle of 33° above the horizontal is approximately937.7 N.

To find the tension in each rope, we can use the fact that the net force in the vertical direction must be zero since the person in the hammock is at rest. Let T1 and T2 be the tensions in the ropes, and let the x-axis point to the right and the y-axis point upward.

A) The forces acting on the person are their weight (mg) downward and the tensions T1 and T2 in the two ropes, which make angles θ1 and θ2 with the horizontal.

The vertical components of the tensions are T1sinθ1 and T2sinθ2, respectively, and the horizontal components are T1cosθ1 and T2cosθ2.

Therefore, we can write:

T1sinθ1 + T2sinθ2 = mg (vertical equilibrium)

T1cosθ1 = T2cosθ2 (horizontal equilibrium)

Solving for T1 and T2, we get:

T1 = (mgcosθ2) / (sinθ1cosθ2 + sinθ2cosθ1)

T1 = (66)(9.81 )(cos(33°)) / (sin(10°)cos(33°) + sin(33°)cos(10°))

T1 ≈ 798.5.4 N

B) Similarly, we can use the horizontal equilibrium equation to find T2:

T2 = T1cosθ1 / cosθ2 = (798.5 N)(cos(10°)) / cos(33°) ≈ 937.7 N

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A lunar eclipse can only occur during a full moon because it is the only time when the sun, Earth, and moon are in the right positions for the Earth's shadow to fall on the moon.

A lunar eclipse can only happen during a full moon because of the relative positions and alignments of the Earth, the moon, and the sun.

During a lunar eclipse, the Earth passes between the sun and the moon, casting its shadow on the moon.  For the Earth's shadow to fall on the moon, the sun, Earth, and moon must be nearly aligned, with the Earth in the middle. This alignment only occurs during a full moon, when the moon is on the opposite side of the Earth from the sun.

During a full moon, the sun illuminates the entire visible face of the moon, making it appear fully round and bright in the sky. If the alignment is just right, the Earth's shadow can fall on the moon, causing a lunar eclipse.

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When investigating a crime scene, it is crucial to gather as much evidence as possible to understand what happened. In this case, the investigator found bullet holes in the wall out the window, indicating that a weapon was fired horizontally. By analyzing the trajectory of the bullet, the investigator can determine at what height the weapon was fired.

One way to do this is by measuring the angle of the bullet holes in relation to the ground. If the bullet holes are at a lower angle, it suggests that the weapon was fired from a lower height. Conversely, if the bullet holes are at a higher angle, it indicates that the weapon was fired from a higher height.

Another way to determine the height of the weapon is by examining the location of the bullet holes on the wall. If the bullet holes are located closer to the ground, it suggests that the weapon was fired from a lower height. On the other hand, if the bullet holes are located higher up on the wall, it indicates that the weapon was fired from a higher height.

Knowing the height of the weapon can provide important insights into the crime. For example, if the weapon was fired from a low height, it suggests that the perpetrator was in close proximity to the victim. Conversely, if the weapon was fired from a high height, it could indicate that the perpetrator was located at a distance from the victim.

Overall, determining the height at which the weapon was fired is an important piece of evidence that can help investigators piece together what happened at the crime scene. By analyzing the trajectory of the bullet and the location of the bullet holes, investigators can gain valuable insights that can help them solve the crime.

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To estimate the maximum number of cars that can safely travel on a road at a given speed, the traffic fanatic should consider the free-flow speed, headway between cars at different speeds, and other factors affecting traffic flow.

The traffic fanatic's assumption is based on the concept of traffic flow theory, which aims to understand and predict the behavior of traffic on a road network. The safe distance between cars is known as the "headway" and it is dependent on the speed of the cars.

The traffic flow theory proposes that the maximum traffic flow occurs at a certain speed called the "optimal speed" or "free-flow speed". At this speed, the headway between cars is minimized, and the maximum number of cars can safely travel on the road.

The function N(s) represents the number of cars that can pass a given spot per minute at a given speed s. In this case, the function is modeled as N(s) = 150, which means that the maximum number of cars that can pass the given spot per minute is 150, regardless of the speed.

However, in reality, the number of cars that can pass a given spot per minute varies with speed. At speeds lower than the free-flow speed, the headway between cars increases, and the number of cars that can pass the given spot decreases. At speeds higher than the free-flow speed, the headway between cars decreases, and the number of cars that can pass the given spot also decreases due to increased congestion and potential accidents.

Therefore, to estimate the maximum number of cars that can safely travel on a particular road at a given speed, the traffic fanatic should consider the free-flow speed and the headway between cars at different speeds. She can use traffic flow models such as the Greenshields model or the Underwood model to estimate the traffic flow at different speeds and densities.

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The person's displacement is closest to 7.1 kilometers.

To find the displacement of the person, we can use the Pythagorean theorem.

The person walks 5.0 km north and 5.0 km east. This creates a right triangle with sides of length 5.0 km and 5.0 km.

Using the Pythagorean theorem, we can find the length of the hypotenuse, which is the displacement of the person:

displacement = √(5.0 km)^2 + (5.0 km)^2

displacement = √(25 km^2 + 25 km^2)

displacement = √50 km^2

displacement = 7.1 km (rounded to one decimal place)

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Answer:

yes

Explanation:

Answer:A

Explanation:

The magnitude of the resultant displacement of Mac and Tosh is 107.0 m, and the direction is northeast (45°).

Displacement is a vector quantity that describes the change in position of an object over time. It is the difference between the initial and final positions of an object, measured in a given direction. Displacement is a measure of the distance moved, regardless of the direction in which the object is traveling. In physics, displacement is a fundamental concept used to describe the motion of particles and objects. It is used to calculate the change in position of an object over a certain period of time and is used to describe the motion of objects in one-dimensional motion. It is also used to calculate the velocity and acceleration of an object.

North-South component = 35.0 m - 54.5 m = -19.5 m
East-West component = 65.0 m - 30.5 m = 34.5 m
Next, we use the Pythagorean theorem to calculate the magnitude of the resultant displacement:
Magnitude = √(-19.5 m)² + (34.5 m)² = √758.25 m = 107.0 m
Finally, we calculate the direction of the displacement from the ratio of the North-South component to the East-West component:
Direction = tan-1(-19.5 m/34.5 m) = -45°
Therefore, the magnitude of the resultant displacement of Mac and Tosh is 107.0 m, and the direction is northeast (45°).

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The most useful quantity you could give the police in this situation is the burglar's: Velocity.

Explanation:
1. Velocity: It provides both the speed and direction of the burglar, which would be helpful for the police to track and catch them.
2. Acceleration: It refers to the rate of change in velocity, but it wouldn't be as helpful without knowing the initial velocity and direction.
3. Time: It's not particularly helpful in this situation, as it does not give any information about the burglar's movement.
4. Speed: While it gives the rate of movement, it lacks the direction, which is crucial for the police to know where the burglar is headed.

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If you had 3.8 x 10^22 J of energy and a machine that could turn all of that energy into mass, your mass would be approximately 4.23 x 10^5 kg.

To find the mass, we will use the mass-energy equivalence formula, which is represented by the famous equation E=mc^2. Here, E is the energy, m is the mass, and c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s).

Step 1: Given energy, E = 3.8 x 10^22 J

Step 2: Speed of light, c = 3.00 x 10^8 m/s

Step 3: Rearrange the equation E=mc^2 to solve for mass: m = E / c^2

Step 4: Plug the given energy and speed of light into the equation: m = (3.8 x 10^22 J) / (3.00 x 10^8 m/s)^2

Step 5: Calculate the mass: m = (3.8 x 10^22 J) / (9 x 10^16 m^2/s^2) = 4.23 x 10^5 kg

So, if you were able to convert all 3.8 x 10^22 J of energy into mass, the resulting mass would be approximately 4.23 x 10^5 kg.

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The angle of refraction is 19.2 degrees. The angle of refraction can be calculated using Snell's law, which states that n1sin(theta1) = n2sin(theta2), where n1 and n2 are the indices of refraction of the two mediums and theta1 and theta2 are the angles of incidence and refraction respectively.

In this case, the incident medium is air with an index of refraction of approximately 1, and the refractive index of crown glass is around 1.52. Therefore, we can write:

1sin(30.0°) = 1.52sin(theta2)

Solving for theta2, we get:

theta2 = sin⁻¹(1sin(30.0°)/1.52) = 19.2°

Therefore, the angle of refraction is 19.2 degrees.

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Answer:

Three states of matter exist—solid, liquid, and gas. Solids have a definite shape and volume. Liquids have a definite volume,

Explanation:

According to the information, the table is completed as follows: Do they have definite shape? no (vapor), no (water), yes (ice); Do they have definite volume? no (vapor), yes (water), yes (ice); Do they compress? yes (vapor), no (water), no (ice).

To fill the table to describe the characteristics of the states of matter we have to look for additional information of each state of matter and then complete the table. According to the information we can infer that the correct way to complete the table is:

Do they have definite shape? no (vapor), no (water), yes (ice); Do they have definite volume? no (vapor), yes (water), yes (ice); Do they compress? yes (vapor), no (water), no (ice).

Vapor | No | No | Yes

Water | No | Yes | No

Ice | Yes | Yes | No

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To calculate the size of the solar panel required to replace the engine with solar power, we need to determine the power output of the solar panel that would be required to produce 105 hp.

First, we need to convert 105 hp to watts:

105 hp x 746 W/hp = 78,330 W

Next, we need to determine the area of the solar panel required to produce 78,330 W of power, assuming a solar panel efficiency of 20%:

78,330 W / 0.20 = 391,650 W

To convert this power to solar irradiance in W/m^2, we need to divide it by the maximum solar energy that reaches the Earth's surface, which is 1000 W/m^2:

391,650 W / 1000 W/m^2 = 391.65 m^2

Therefore, we would need a solar panel with an area of approximately 391.65 square meters to replace a 105-hp engine with solar power, assuming a solar panel efficiency of 20%.

1. False.

Gravity is a non-contact force that acts between two objects with mass, even if they are not in physical contact with each other.

2. False.

Gravity is the force exerted by the Earth (or any other massive body) on an object with mass.

The weight of an object is the measure of the force of gravity acting on it, and it is equivalent to the mass of the object times the acceleration due to gravity.

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Mike does approximately 303.2175 joules of work on the mower each time he pushes it 9.1 meters across the yard.

To calculate the work done by Mike on the mower, we can use the formula:

Work = Force * Distance * cos(theta)

where:

Given:

Force = 45 N

Distance = 9.1 m

theta = 41°

Converting the angle to radians:

theta_rad = 41° * (π/180) ≈ 0.7156 radians

Calculating the work:

Work = 45 N * 9.1 m * cos(0.7156)

Work ≈ 45 N * 9.1 m * 0.7483

Work ≈ 303.2175 J

Therefore, Mike does approximately 303.2175 joules of work on the mower each time he pushes it 9.1 meters across the yard.

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A two-pole AC motor operates on a three-phase, 60 Hz, 240 Vrms line-to-line supply.The answer is option B, 1800 rpm.

This is because the synchronous speed of a two-pole AC motor is given by the formula:

Synchronous speed (in RPM) = (120 x Frequency) / Number of poles

In this case, the frequency is 60 Hz and the number of poles is 2.

Synchronous speed = (120 x 60) / 2 = 3600 rpm

However, this is the theoretical speed that the motor would operate at if there was no load or slip. In reality, the motor will experience some slip, which means that its actual operating speed will be slightly less than the synchronous speed.

Therefore, the correct answer is option B, 1800 rpm, which is slightly less than the synchronous speed of 3600 rpm.

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The momentum of an object is defined as the product of its mass and velocity. The momentum of the larger truck is the same as the momentum of the smaller truck, even though the larger truck has more mass and less velocity.

Therefore, the momentum of an object can be calculated using the formula:

momentum = mass x velocity

In this problem, we have two trucks. Let's call the smaller truck A and the larger truck B. We are given that truck A has a velocity of 20 m/s. We are also told that truck B has twice the mass of truck A, but is traveling at half the speed. This means that the velocity of truck B is:

velocity of truck B = 1/2 x 20 m/s = 10 m/s

Using the formula for momentum, we can calculate the momentum of each truck:

momentum of truck A = mass of truck A x velocity of truck A

momentum of truck B = mass of truck B x velocity of truck B

Since truck B has twice the mass of truck A, we can substitute 2m for mB in the second equation:

momentum of truck A = mAx20 m/s = 20mA

momentum of truck B = (2m)x10 m/s = 20m

Comparing the two equations, we see that the momentum of truck B is equal to the momentum of truck A. Therefore, the momentum of the larger truck is the same as the momentum of the smaller truck, even though the larger truck has more mass and less velocity.

In summary, the momentum of an object is the product of its mass and velocity. The momentum of the larger truck is the same as the momentum of the smaller truck, even though the larger truck has more mass and less velocity.

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To answer your question about the distance traveled by light from the left slit compared to the right slit, we can use the formula for constructive interference in a double-slit experiment.

The formula for the path difference is given by:

ΔL = m * λ

where ΔL is the path difference (the extra distance traveled by light from the left slit compared to the right slit), m is the order of the maximum (m=1 in this case), and λ is the wavelength of the light (550 nm).

Now, we can plug in the values:

ΔL = 1 * 550 nm

ΔL = 550 nm

So, the light from the left slit traveled 550 nm farther than the light from the right slit in reaching the m=1 maximum on the right side of the central maximum.

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Answer:

time: seconds

length: meter

mass: kilogram

electric current: ampere

temperature: Kelvin

Explanation: