The magnitude of the vector sum of 2x and 3y is determined as 3.6 units and the direction is 56.3⁰.
Magnitude of the vector
The magnitude of two vectors is determined using the following formula;
[tex]|V| = \sqrt{V_x^2 + V_y^2}[/tex]
Let the sum of the vector = 2x + 3y
The magnitude of the vectors is calculated as follows;
[tex]|V| = \sqrt{2^2 + 3^2} \\\\|V| = 3.6 \ units[/tex]
Direction of the vectorsThe direction of the vectors is calculated as follows;
[tex]tan(\theta) = \frac{V_y}{V_x} \\\\tan(\theta) = \frac{3}{2} \\\\tan(\theta) = 1.5\\\\\theta = tan^{-1} (1.5)\\\\\theta = 56.3 \ ^0[/tex]
Thus, the magnitude of the vector sum of 2x and 3y is determined as 3.6 units and the direction is 56.3⁰.
Learn more about vectors here: https://brainly.com/question/25705666
#SPJ1
“Jonny pulls his sister Jane (weight 28 lbs), who is sitting in a wagon, up an incline ramp (θ = 17°) with a steady speed. If the coefficient of kinetic friction is 0.18, the wagon has a mass of 14 kg, and the length of the ramp is 2.4 m, find: a) the work done by the frictional force. b) the work done by the gravitational force.“
(a) The work done by the frictional force is -33.1 J.
(b) The work done by the gravitational force is 175.58 J
Work done by frictional force
The work done by frictional force is calculated as follows;
W = -μmgsinθ x L
W = -μmgsinθ x L
where;
m is mass of Jane and wagonW = -0.18 x (12.7 + 14)9.8 x sin(17) x 2.4
W = -33.1 J
Work done by the gravitational forceW = mgh
W = mgcosθ x h
W = mgcosθ x Lsinθ
W = (26.7)(9.8)cos(17) x 2.4 x sin(17)
W = 175.58 J
Learn more about work done here: https://brainly.com/question/8119756
#SPJ1
A transverse wave on a string has an amplitude of 20 cm, a wavelength of 35 cm, and a frequency of 2.0 Hz. The wave moves in the positive x-direction.
--Enter any fractional coefficients as fractions, i.e., do not approximate fractions using decimals. Enter as itself; do not multiply it with other numerical factors. Enter phase angles in inverse function form if they do not evaluate one of the special angles on the unit circle.
--Write the mathematical description of the displacement y1(x,t) from equilibrium for the wave if, at t=0, x=0, and y1=0.
y1(x,t)= ___m
--Write the mathematical description of the displacement y2(x,t) from equilibrium for the wave if, at t=0, x=0, and y2=20 cm.
y2(x,t)= ___m
Write the mathematical description of the displacement y3(x,t) from equilibrium for the wave if, at t=0, x=0, and y3=−20 cm.
y3(x,t)= ___m
Write the mathematical description of the displacement y4(x,t) from equilibrium for the wave if, at t=0, x=0, and y4=13 cm.
y4(x,t)= ___m
(a) The mathematical description of the displacement of the wave, y1(x,t) = 0.2 m.
(b) The mathematical description of the displacement of the wave, y2(x,t) = 0.4 m.
(c) The mathematical description of the displacement of the wave, y3(x,t) = 0.2 m
(d) The mathematical description of the displacement of the wave, y4(x,t) = 0.33 m
Wave functionThe general wave function is written as follows;
y(x, t) = Acos(kx - ωt)
where;
k is the wave number = 2π/λA is amplitude of the wave = 20 cmω is angular speedλ is the wave length = 35 cmy0 = Acos(kx - ωt)
y0 = 20cm x cos(0 - 0)
y0 = 20 cm
From equilibrium of the wave, at t=0, x=0, y1 = 0y1(x,t) = 20cm x cos(0 - 0) = 20 cm
y1(x,t)= 20 cm = 0.2 m
Thus, y1 = y1 + y0
From equilibrium of the wave, at t=0, x=0, y2 = 20 cmy2 = y0 + y1 + y2
y2 = 20 cm + 0 + 20 cm
y2(x,t)= 40 cm = 0.4 m
From equilibrium of the wave, at t=0, x=0, y3 = -20 cmy3 = y0 + y1 + y2 + y3
y3 = 20 cm + 0 + 20 cm - 20cm
y3(x,t)= 20 cm = 0.2 m
From equilibrium of the wave, at t=0, x=0, y4 = 13 cmy4 = y0 + y1 + y2 + y3
y4 = 20 cm + 0 + 20 cm -20 cm + 13 cm
y4 = 33 cm
y4(x,t) = 33 cm = 0.33 m
Learn more about equation of wave here: https://brainly.com/question/4692600
#SPJ1
A lamp has a voltage of 120 V across it and uses a current of 0.5A. What is the power used by the lamp?
Given the voltage of the lamp and the amount of current use, the power used by the lamp is 60Watts.
What is the power used by the lamp?Power is the quantity of energy transferred per unit time. It can be expressed as;
P = v × I
Where v is voltage and I is current.
Given that;
Voltage v = 120VCurrent I = 0.5APower P = ?P = v × I
P = 120V × 0.5A
P = 60Watts
Therefore, given the voltage of the lamp and the amount of current use, the power used by the lamp is 60Watts.
Learn more about Ohm's law here: https://brainly.com/question/12948166
#SPJ1
A (-8.8×10-20 C) charge is moving at (9.6×106 m/s) perpendicular a magnetic field. It
experiences a force of to (-5.2×10-16 N). What is the magnetic field strength?
6.2×10 -4 T
5.4×10 -15 T
3.2 ×10 -27 T
4.4×10 -20 T
The magnetic field strength will be 6.1 x 10⁻⁴ T.
What is magnetic field?The magnetic field is the region of space where a charged object experiences magnetic force when it is moving.
The magnetic field strength is the magnitude of magnetic field in Tesla. It is related to velocity, magnitude of charge and force by the relation,
Magnetic force F = qVB
Given is the charge q = -8.8×10⁻²⁰ C, Force F = -5.2×10⁻¹⁶ N and the velocity v = 9.6×10⁶ m/s, then the magnetic field strength will be
B = -5.2×10⁻¹⁶/-8.8×10⁻²⁰ x9.6×10⁶
B = 6.1 x 10⁻⁴ T
Thus, the magnetic field strength will be 6.1 x 10⁻⁴ T.
Learn more about magnetic field.
https://brainly.com/question/14848188
#SPJ1
2. A student was sitting on one end of a set of metal bleachers outside of a school building. A drumline was practicing on the other end of the bleachers. Some of the musicians are drumming on the bleachers while others are drumming on their drums. The drumming on drums doesn’t bother the student, but the drumming on the bleachers does because he can feel it in the seat. He moves further away, which helps, but not enough. Finally, he decides to sit on his backpack. Compare the two types of waves the student is detecting. In your response, be sure to include: Why the student can feel the vibrations from the bleachers, but not from the drums. Identification of the two types of waves created by the drumming. A description of two similarities between the two wave types A description of two differences between the two wave types. Why moving away and sitting on the backpack helps him feel the waves less.
The students can feel the vibrations from the bleachers, but not from the drums because of the resonance.
What is the resonance?The resonance condition occurs when the frequency of a wave matches with the resonance frequency.
The transfer of energy becomes maximum when the natural frequency matches with the frequency generated by the source.
The bleacher and student together having the frequency matching with the resonance frequency of the drum.
The bleacher and student with the bag frequency doesn't match with the resonance value of drums. Secondly, as distance increases sound intensity also decreases.
Thus, the student can feel the vibrations from the bleachers, but not from the drums because of the resonance.
Learn more about resonance.
https://brainly.com/question/15337338
#SPJ1
What affect does distance have on an electric field?
The closer an uncharged particle is to an electric field, the stronger the force exerted.
The further an uncharged particle is from an electric field, the stronger the force exerted.
The further a charged particle is from an electric field, the stronger the force exerted.
The closer a charged particle is to an electric field, the stronger the force exerted.
Answer:
the answer is equal to yes
Nisha stands at the edge of an aquarium 3.0 m deep. She
shines a laser at a height of 1.7 m that hits the water of the pool
8.1 m from the edge. How far from the edge of the pool will the light hit bottom?
It's denoting to a right angle traingle
Perpendicular=P=3+1.7=4.7mBase=B=8.1mHypotenuse we need
Apply Pythagorean theorem
H²=P²+B²H²=4.7²+8.1²H²=87.7H=9.4mExplanation:
The graph of y = √x is reflected in the y-axis, is horizontally stretched by a factor of 2, shifted 3 units up and 1 unit left. What is the equation of the transformed graph?
Original: y = √(x)
Reflected in the y-axis: y = √(-x)
Horizontally stretched by a factor of 2: y = √(-x/2)
Shifted 3 units up: y = 3 + √(-x/2)
And 1 unit left: y = 3 + √(-(x+1)/2)
What's the temperature 414 K in degrees Celsius?
Answer:
140.85 is the correct answer
Find the radius and the circumference to the nearest hundredth when d ≈ 3.6 in. Use 3.14 for π. Drag and drop the correct number into each box to complete the answers.
The radius is approximately _ inches.
The circumference is approximately _ inches.
Explanation:
the radius is always half of the diameter.
so, the radius is approximately 3.6/2 = 1.8 in.
and the circumference of a circle is
2×pi×r = d×pi = 3.6×3.14 = 11.304 ≈ 11.3 in.
How do you know that light travels faster than
sound? (Hint: Give an example of something that
produces sound and light at the same time.)
Answer:
Explanation:
Answer
How about a thunder storm. I don't know if you live in a city or out in the sticks as I do. Lighting is very obvious and it is not a good idea to be out when experiencing a thunderstorm, especially in an open field. You might be the only thing around that will cause the lightning to be connected to the ground.# Seconds later, you will hear the thunder which is quite harmless. If you live in the city, observing this is not quite so easy. There are all kinds of buildings around and some of them may block your view.
#The great golfer, Lee Travino, was "hit" by lightening storm twice while playing in tournaments.
1. The Falcon Heavy rocket takes off with a constant net vertical force of 6.27 x 10^5
N. How much work does it do if it moves a distance of 144 km?
Explanation:
The formula for work is
[tex]w = |f| |d| \cos(x) [/tex]
where x is the angle between the displacement and force.
F is the force that is currently being active.
D is the displacement.
We only want our force and displacement to be positve so we use the absolute value sign.
Since the rocket and the displacement is both upwards, the signs. between them is 0.
So since
[tex] \cos(0) = 1[/tex]
We can just use that
[tex]w = |f| |d| [/tex]
First, we covert km to m.
[tex]144 \: km \times \frac{1000 \: m}{1 \: km} = 144000 m[/tex]
Now, we can multiply.
[tex]w = 14400 \: km \: \times (6.27 \times 10 {}^{5} )[/tex]
[tex]w = (1.44 \times 10 {}^{5} ) \times (6.27 \times 10 {}^{5} )[/tex]
[tex]w = 9.0288 \times 10 {}^{10} [/tex]
N times Meters = J so our answer is
[tex]w = 9.0288 \times 10 {}^{10} \: j[/tex]
- A particular light source gives off light waves with a measured wavelength of
2.0 X 10-7m. What is the frequency of the light source?
Answer:
f = 1.5 x 10¹⁵ Hz
Explanation:
Light is an electromagnetic wave and we know that the speed of light is a constant which is
3 x 10⁸ m/s.
Knowing this; v = λ x f
λ = wavelength
f= frequency of light
v = seed of light
f = v/λ
f = 3 x 10⁸m/s / 2.0 x 10-⁷ m
f = 1.5 x 10¹⁵ Hz
If humans are exposed to radiation, this can cause a change in their DNA base sequence. What is the term given to this?
The term used to indicate different DNA nucleotide changes in humans exposed to radiation is called a mutation.
What is a mutation?A mutation is any DNA nucleotide change or modification that occurs in the genome of a given organism.
Mutations may be caused by physical agents (e.g., UV radiation) or chemical agents.
In conclusion, the term used to indicate different DNA nucleotide changes in humans exposed to radiation is called a mutation.
Learn more about mutations here:
https://brainly.com/question/17031191
#SPJ1
what is 7 times 7 times 7 plus 3
6) If the mass of an object is 28kg and the gravitational force is 18G, what is the gravitational force of an object
that has half the mass?
a. 14kg
b. 56kg
C. 9G
d. 36G
Answer:
The gravitational force of an object that has half the mass is C) 9G.
Explanation:
Newton's Law of Gravitation:
[tex]\displaystyle F_g=G\frac{Mm}{r^2}[/tex]We can see that the gravitational force, [tex]F_g[/tex], and mass (let's combine M * m into just "m"), [tex]m[/tex], are directly proportional to each other.
This means that if [tex]F_g[/tex] increases, [tex]m[/tex] also increases.
Therefore, if the mass is halved, that means that the gravitational force is also going to be halved.
The answer is 18G / 2 = 9G, which corresponds to answer C) 9G.
3- Which of the following represents a way through which thermal energy is transferred by direct contact?
a Conduction O
b. Radiation O
c. Convection O
d. Specific heat
Answer:
A. conduction
Explanation:
Conduction is the transfer of energy from one molecule to another by direct contact.
The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :
x=-3.5sin(π/2t+(5π)/4)
Find
a. maximum kinetic energy
b. maximum potential energy
c. maximum mechanical energy
The maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.
What is simple harmonic motion?Simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.
Simple Harmonic Motion
The given equation of the simple harmonic motion is
[tex]x=3.5 sin (\frac{\pi }{2t} + \frac{5\pi }{4} )[/tex]
Data;
ω = π/2
k = 1.254N/m
Solving this
[tex]\frac{dx}{dt} = -3.5 X \frac{\pi }{2} cos (\frac{x\pi t}{2}+\frac{5\pi }{4} )[/tex]
Let's calculate the maximum velocity.
[tex]V_{m} =\frac{3.5\pi }{2}[/tex]
This is only possible when cos θ = -1
The maximum kinetic energy is
[tex]K_m =\frac{1}{2} mv^2 = \frac{1}{2} X \frac{500}{1000} X \frac{7^2\pi ^2}^{4} ^2[/tex]
[tex]w^2 = \frac{k}{m} \\k = w^2m\\k = \frac{\pi ^2}{4} X \frac{500}{1000} \\k =1.254 N/m[/tex]
Using the value of spring constant, we can find the maximum potential energy.
[tex]P.E =\frac{1}{2} k x^2\\P.E =\frac{1}{2} X 1.234 X 3.5^2 \\P.E = 7.56 J[/tex]
The maximum potential energy is 7.56J
The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.
ME = K.E + P.E
ME = 7.56J
From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.
Learn more on simple harmonic motion here;
brainly.com/question/15556430
#SPJ1
A particle q1 with the charge of 4.5x10-⁶C is fixed in the space from a distance of 3.7cm , a particle q2 of mass 6.9g and the charge of -3.10x10-⁶C is fired with the initial velocity of 60m/s toward the fixed charge. what is the velocity when it is 1cm away from the q1
The velocity of particle 2 when it is 1cm away from particle 1 is determined as 62.18 m/s.
Force between the charges
The electrostatic force between the two charges is calculated as follows;
F = (kq1q2)/(r²)
F = (9 x 10⁹ x 4.5 x 10⁻⁶ x 3.1 x 10⁻⁶)/(0.037)²
F = 91.71 N
Acceleration of the second particleF = ma
a = F/m
a = (91.71 N)/(0.0069 kg)
a = 13,291.2 m/s²
Velocity of particle 2 at 1 cm from particle 1v² = u² + 2as
v² = 60² + 2(13,291.2)(0.01)
v² = 3865.82
v = 62.18 m/s
Learn more about velocity here: https://brainly.com/question/6504879
#SPJ1
In sound, the wavelength of the sound
determines the __ of the sound.
A. Pitch
B. Volume
C.Length
Answer:
A) Pitch
Explanation:
Wavelength determines the pitch ( or frequency which is 1/wavelength)
why Neil deGrasse Tyson says NASCAR doesn’t like the Doppler effect.
We can confirm that Neil deGrasse Tyson made this claim due to the fact that NASCAR races use speakers with the sounds of the race.
Why would using speakers ruin the Doppler effect?The Doppler effect in regards to sound is a shift in the way we hear the sound as the object is coming closer and then moving farther away, something that NASCAR cars do very often during races. Placing speakers would overlap this sound with a constant sound wave, making the audience unable to perceive the doppler effect.
Therefore, we can confirm that Neil deGrasse Tyson made this claim due to the fact that NASCAR races use speakers with the sounds of the race.
To learn more about the Doppler effect visit:
https://brainly.com/question/9165991?referrer=searchResults
A force of 124 newtons pushed a 12kg object forward 13 meters. How much work is being done?
Answer:
Work = Force * Distance
Here,
force = 124 N
distance = 13m
Thus, Work = 124 * 13 = 1612 joules(J)
Please just give me an answer, thanks.
1. task
The resistance of the light bulb is 0.4 kΩ. To what voltage is it connected if a current of 33 mA flows through it? The answer is rounded to the nearest whole number!
2. task
The length of the cable is 69 m, its cross-sectional area is 0.4 mm2. What material is the wire made of if its resistance is 86.3 Ω? Just give me the result of numbers, i'll find myself what material corresponds to those numbers
3. task
Calculate the resistance of the galvanometer if a current of 6 μA flows through it and the voltage is 7 mV! Round to the nearest whole number!
#1
[tex]\\ \rm\dashrightarrow P=VI\implies V=\dfrac{P}{I}[/tex]
[tex]\\ \rm\dashrightarrow V=\dfrac{0.4\times 10^3}{33\times 10^{-3}}[/tex]
[tex]\\ \rm\dashrightarrow V=0.012\times 10^{-6}[/tex]
[tex]\\ \rm\dashrightarrow V=12mV[/tex]
#2
[tex]\\ \rm\dashrightarrow R=\rho \dfrac{\ell}{A}[/tex]
[tex]\\ \rm\dashrightarrow \rho =\dfrac{RA}{\ell}[/tex]
[tex]\\ \rm\dashrightarrow \rho=\dfrac{86.3(0.4\times 10^6)}{69}[/tex]
[tex]\\ \rm\dashrightarrow \rho=0.5\times 10^{6}[/tex]
It should be silicon#3
Ohms law
[tex]\\ \rm\dashrightarrow R=\dfrac{V}{I}[/tex]
[tex]\\ \rm\dashrightarrow R=\dfrac{7(10^3)}{6(10^{-6})}[/tex]
[tex]\\ \rm\dashrightarrow R=1.167\times 10^9\Omega[/tex]
A body moves in the east with the velocity of 25 m/s. Another body B moves in the same direction with a velocity of 10 m/s. If both of them had started from the same point then find :
i) The velocity of w .r. t. B.
ii) The distance covered by each in 30
seconds...
iii) The distance between them after 1
minute...
Please help....ty !!!
[tex].....[/tex]
Answer:
See below
Explanation:
i) Velocity of A wrt B is 15 m/s east
ii) A 30 * 25 = 750 m east B 30 *10 = 300 m east
iii) 1 minute will be 15 m/s * 60 = 900 m apart
3. The height of a wave crest is called
a. wavelength.
c. amplitude.
b. frequency
d. energy
Answer:
C. Amplitude
Explanation:
During which weeks of the moon cycle does the moon appear to be getting smaller
Answer:
Since the illuminated side of the moon appears to be getting smaller in size (after the full moon), the moon is said to be in the "erosion phase". For the next 7 days, the moon will remain in an “eroded gibbous stage”.
Explanation:
The drawing shows a crystalline slab (refractive index 2.043) with a rectangular cross section. A ray of light strikes the slab at an incident angle of θ1= 37.0°, enters the slab, and travels to point P. This slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total internal reflection occurs at point P?
A drawing shows a crystalline slab (refractive index 2.043) with a rectangular cross-section, the maximum value of n is mathematically given as
nm=1.627
What is the maximum value of n such that total internal reflection occurs at point P?Generally, the equation for the snells law is mathematically given as
[tex]n=\frac{sin \theta_1}{sin \theta_2}[/tex]
Therefore
[tex]\theta_2=sin-1(sin35/1.725)\\\\\theta_2=19.42[/tex]
From the image critical angle is
ic=90-19.42
ic=70.58
In conclusion, snells law for total internal reflection
[tex]gn=\frac{sinic}{sin90}[/tex]
sinic=nm/ng
nm=1.725*sin70.58
nm=1.627
Read more about Lens
https://brainly.com/question/13644773
#SPJ1
Velocity can be negative, but kinetic energy cannot. Why?
Because of the formula
Let's see
how
KE=1/2mv²m is mass
v is velocity
as it's v²
Its must be greater than or equal to 0 ,So kinetic energy can't be negative
The crust is composed primarily of basalt and _____________.
Answer:
Granite
Explanation:
Trust me I learned this 2years ago
What is the acceleration when a force of 2.0N is applied to a ball that has a mass of 0.60 Kg ?
Formula :- Force = mass × acceleration
F= m × a
[tex]2 = 0.6 \times a \\ 2 \times \frac{10}{6} = a \\ \cancel2 \times \frac{10}{ \cancel6 {}^{ \: \: 3} } = a \\ \frac{10}{3} = a = 3.33[/tex]
Option A -> 3.3
Answer:
3.3 m/s²
Explanation:
Formula :
Force = mass × accelerationGiven :
Force (F) = 2.0 Nmass (m) = 0.60 kgSolving :
2.0 N = 0.60 kg × acceleration (a)a = 2.0/0.60a = 20/6 = 10/3a = 3.3 m/s²HELP I DEPEND ON THIS
Answer:
D. A force within a fluid that pushes upward
Explanation:
Buoyancy is the ability of something floating in water, so it's probably not about the attraction between molecules and is about a force within a fluid. If a force within a fluid is pushing downwards on an object, that would make the object go downwards (sink), which is not buoyancy. If a force within a fluid is pushing upwards on an object, the object would be floating.
Answer:
Option D
Explanation:
When you put any object and push it inwards water .
According to Newton's third law every action has equal and opposite reaction
So the water hits back with opposite force which is known as buoyant force.
Archimedies law is applicable in these cases
