A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm . The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony?

Answers

Answer 1

The physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.

How fast was the physicist traveling, according to his own testimony?

Using the formula for doppler shift for light,

λ' = λ√[(1 + v/c)/(1 - v/c)] where

λ = wavelength of source, λ' = wavelength of observer, v = speed of source and c = speed of light

Given that the driver is moving away from the stop light, we take the driver as the source. Since, the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm. we have

λ' = wavelength of source = 650 nm, λ' = wavelength of observer = 520 nm

So, substituting the values of the variables into the equation, we have

λ' = λ√[(1 + v/c)/(1 - v/c)]

520 nm = 650 nm√[(1 + v/c)/(1 - v/c)]

520/650 = √[(1 + v/c)/(1 - v/c)]

0.8 = √[(1 + v/c)/(1 - v/c)]

Squaring both sides, we have

0.8² = (1 + v/c)/(1 - v/c)

0.64 = (1 + v/c)/(1 - v/c)

0.64(1 - v/c) = (1 + v/c)

0.64 - 0.64v/c = 1 + v/c

0.64 - 1 = v/c + 0.64v/c

-0.36 = 1.64v/c

-0.2195 = v/c

v = -0.22c

v = -0.22 × 3 × 10⁸ m/s

v = -0.66 × 10⁸ m/s

v = -6.6 × 10⁷ m/s

So, the physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.

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Related Questions

while driving on a two lane highway, you come across a sharp curve and see a large, slow moving vehicle

Answers

Use manual gearbox to lessen the impact of force.

since we have not much space to maneuver we will identify all the possible sources.

through this sources try to minimize the damage as much as possible

Firstly we will try this :

1)

The car would try to slow down as much as it could and avoid the collision if it had a manual gearbox.

Second option could be:

2)

On the other hand, if the automobile has an automatic transmission, try to stop as hard as you can, but just before you strike the truck, to prevent going under it and lessen the force of the contact.

Last resort should be:

3)

The handbrake may also be engaged as a third option, which would cause my car to turn and attempt to avoid hitting the other car.

In case the highway is not barricaded on left side as an emergency measure we could crash off road.

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a 6.96 nc charge is located 1.82 m from a 4.02 nc point charge. (a) find the magnitude of the electrostatic force that one charge exerts on the other. n (b) is the force attractive or repulsive? attractive repulsive

Answers

The electric force is 7.60 x 10¯⁸ N.

We need to know about the electrostatic force to solve this problem. The electrostatic force produced by charges interacting each other, whose strength is given by the equation

F = k.Q1 . Q2/r²

where F is the electrostatic force, Q1 and Q2 is the charge and r is the radius.

From the question above, we know that

k = 9 x 10⁹ Nm²/C²

Q1 =e = 6.96 x 10¯⁹ C

Q2 = e = 4.02 x 10¯⁹ C

r = 1.82 m

The electrostatic force will attract each other when the charges are different and will repel each other when the charges are same.

F = k.Q1 . Q2/r²

F = 9 x 10⁹ . 6.96 x 10¯⁹ . 4.02 x 10¯⁹/1.82²

F = 7.60 x 10¯⁸ N

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An arrow is shot horizontally at 93 m/s, from a height of 0.80 meters. Calculate the amount of time (in seconds) the arrow is in the air. Round to two decimal places.

Answers

.90m = .70g = .45 yes

Chemical molecules called ___________ are released at the end of the __________, which allows the neuron to communicate with other neurons.

Answers

Chemical molecules called neurotransmitters are released at the end of the synaptic junction, which allows the neuron to communicate with other neurons.

In the human body, neurotransmitters are chemical messengers that convey information between neurons.

The main function of these transmitters is to pass on electrical signals from nerve cells to other cells of the body including nerves, muscles, and glands.

Neurotransmitters are the major constituents of the nervous system and play a significant role in communication among different organs.

Moreover, they are also crucial for human development and growth.

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Two science teachers challenge each other to a 100m race across the football field.

The loser will grade the winner's science labs for one month. Mrs. Boulware runs the race in 10.40 s. Mrs. Hill runs the first 25.0 m with an average speed of 10.0 m/s, the next 50.0m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of 11.1 m/s. Who gets stuck grading science labs for the next month?

Answers

найдем время, за которые Миссис хилл пробежала первые 25 метров :

T= s/v = T1+T2+T3 + .....

T1=25/10=2.5 секунд - 1/4 от всей дистанции. Найдем T2 по такому же принципу:

T2=50/9.5 = 5.3 секундный - заняли у Хилл, чтоб пробежать следующие 50 метров, найдем T3:

T3=25/11.1=2.25 секунд - последние 1/4 от всей дистанции. Найдем общее время:

T= 2.5+5.3+2.25=10.05 секунд

10.05<10.4, следовательно Мисс Булвер ЛУЗЕР.

a meteoroid changed velocity from 9 to 21 in 13 seconds. What is the acceleration of the meteoroid? (round to the nearest whole number)

Answers

Answer:

Acceleration:

a = 1  km/c²

Explanation:

Given:

V1 = 21 km/h

V2 = 9 km/h

Δt =13 s

________________

a - ?

a =(V2 - V1) / Δt = (21 - 9 ) /13 = 12 /13 ≈ 1  km/c²

use the drop-down menu to complete the statement. the production of an electric current by a changing magnetic field is known as .

Answers

The production of an electric current by a changing magnetic field is known as electromagnetic induction.

The phenomenon when the current is produced due to changing magnetic field is given by Faraday.

And this phenomenon is called the electro-magnetic induction or magnetic induction since the electricity is generated due to the fluctuations or variance in the magnetic field.

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Answer:

electromagnetic induction

Explanation:

If two objects have the same mass which is more
dense?

Answers

Answer: If two objects have the same mass but have different sizes, the object with the greatest density will be the smaller of the two objects. Using an example of two cubes.

Explanation:

Answer:

the smaller of the two objects

Explanation:

If two objects have the same mass but have different sizes, the object with the greatest density will be the smaller of the two objects.

Suppose you are transported to a planet with twice the mass of earth, but the same radius of earth. Your weight would __________ by a factor of __________.

Answers

According to gravitational force, the weight would be greater by a factor of 2.

We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as

F = G.m1.m2 / R²

where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.

From the question above, we know that

m1 = m

m2 = 2m1 = 2m

R1 = R2 = R

Gravitational force is proportional to mass

F1 ~ M

Hence, the ratio of weight is

F2 / F1 = m2 / m1

F2 / F1 = 2m / m

F2 / F1 = 2

Hence, the weight would be greater by factor of 2 .

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A model shows that the moon has grown to twice its size, yet it has remained in the same place. In one to two sentences, explain how this would impact the gravity between Earth and the moon

Answers

When chromium is added to colorless corundum, a red ruby is born, and a green emerald emerges when chromium is added to colorless beryl.

What is chromium?

Chromium is a chemical element with the atomic number 24 and the symbol Cr. It is the initial component of group 6. It is a transition metal that is glossy, steely-grey, tough, and brittle.

Because of its high level of corrosion resistance and hardness, chromium metal is prized. The discovery that steel could be transformed into stainless steel, which is extremely resistant to corrosion and discoloration, was a significant advancement in the manufacture of steel. Together, stainless steel and chrome plating (chromium electroplating) account for 85% of commercial use. Chromium is highly prized as a metal that can be thoroughly polished while retaining its shine. Over 90% of infrared light and nearly 70% of the visible spectrum are reflected by polished chrome.

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can a car moving towards right have acceleration towards left?

Answers

Answer:

Yes it is possible to have acceleration opposing direction of velocity

Explanation:

1) when you brake the car , the velocity will decrease making the the acceleration to decrease ,it is called decelerating

2) if you imagine the effect of a resistive force or a frictional force than the acceleration is in opposite direction is possible.

A person holds a 0.300 kg pomegranate at the top of a tower that is 96 m high. another person holds a 0.800 kg melon next to an open window 32 m up the tower.

Answers

The gravitational potential energy of the pomegranate is 282.24 J

The gravitational potential energy of the melon is 250.88 J

What do you mean by potential energy?

Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.

The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are examples of common types of potential energy. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).

Although it has connections to the Greek philosopher Aristotle's concept of potentiality, the phrase "potential energy" was coined by the Scottish engineer and physicist William Rankine in the 19th century. Potential energy is connected to forces that affect a body in such a way that their combined work is only dependent on the body's beginning and ultimate positions in space. At any point in space, these forces, also known as conservative forces, can be represented by vectors that are gradients of a particular scalar function known as potential.

Given;

mass of pomegranate, m₁ = 0.3 kg

height of pomegranate, h₁ = 96 m

mass of melon, m₂ = 0.8 kg

height of melon, h₂ = 32 m

The gravitational potential energy of the pomegranate is calculated as;

P.E₁ = m₁gh₁

P.E₁ = 0.3 x 9.8 x 96

P.E₁ = 282.24 J

The gravitational potential energy of the melon is calculated as;

P.E₂ = m₂gh₂

P.E₂ = 0.8 x 9.8 x 32

P.E₂ = 250.88 J

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Pomegranate has a gravitational potential energy of 282.24 J.

Melon has a gravitational potential energy of 250.88 J.

What is potential energy?

Because of its position, an object can store energy. For instance, when kept at an elevated position, the large ball of a demolition machine is storing energy. Potential energy is the name given to this accumulated positional energy. Similar to this, a drawn bow's stance allows it to store energy.

Examples

a boulder perched on a cliff's edge. Potential energy will be transformed into kinetic energy if the rock falls since it will be moving. a longbow with an extended elastic string.

Step by step solution:

Given;

Mass of the  pomegranate, m₁ = 0.3 kg

Height of the  pomegranate, h₁ = 96 m

Mass of the melon, m₂ = 0.8 kg

Height of the melon, h₂ = 32 m

The gravitational potential energy of  pomegranate is calculated as;

P.E₁ = m₁gh₁

P.E₁ = 0.3 x 9.8 x 96

P.E₁ = 282.24 J

The gravitational potential energy of  melon is calculated as;

P.E₂ = m₂gh₂

P.E₂ = 0.8 x 9.8 x 32

P.E₂ = 250.88 J

Hence, Pomegranate has a gravitational potential energy of 282.24 J.

Melon has a gravitational potential energy of 250.88 J.

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When two tuning forks are sounded at the same time, a beat frequency of 5 Hz occurs. If one of the tuning forks has a frequency of 245Hz, what is the frequency of the other tuning fork?(a) 240 Hz (b) 242.5 Hz (c) 247.5 Hz (d) 250 Hz (e) More than one answer could be correct.

Answers

The frequency of other tuning fork can be 240Hz or 250Hz and hence more than one option is correct

A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.

Given that one tuning fork has a frequency of 245Hz

Additionally, it is stated that a 5 Hz is the beat frequency.

We know the beat frequency formula

[tex]f_ {beat}[/tex] = [tex]f_{2}[/tex] -[tex]f_{1}[/tex]

Suppose that the first tuning fork's frequency is equal to [tex]f_{1}[/tex], then

CASE 1:

5= 245- [tex]f_{2}[/tex]

[tex]f_{2}[/tex] =245+5

[tex]f_{2}[/tex] =250 Hz

CASE 2 :

5= 245 + [tex]f_{2}[/tex]

[tex]f_{2}[/tex] =245-5

[tex]f_{2}[/tex] =240 Hz

Hence there is more than one option is correct in the given question

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A scientific law seeks to explain why an event occurred.

Answers

Answer:

answer explanation

Explanation:

explanation answer

If a signal can travel in a cable at 80% of the speed of light, what length of cable, in inches, represents 1 ns?

Answers

According to a signal velocity, the cable length is 9.45 inches.

We need to know about the velocity to solve this problem. The velocity can be determined as the total distance divided by the total time. It can be written as

v = d / t

where v is velocity, d is distance and t is time.

From the question above, we know that

v = 80%c = 0.8c = 2.4 x 10⁸ m/s

t = 1 ns = 1 x 10¯⁹ s

The length of cable can be represented by the distance

v = d / t

d = v . t

d = 2.4 x 10⁸ . 1 x 10¯⁹

d = 0.24 m

Convert to inches (1m = 39.37 inches)

d = 0.24 m

d = 0.24 x 39.37 inches

d = 9.45 inches

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100 points
National Park rangers create public announcements to help prevent accidental wildfires from start. Which is a simple way that accidental wildfires can be prevented in these parks?(1 point)

Ensure people do not have unattended cooking fires while camping.

Ensure people do not create defensible spaces.

Prevent people from thinning dead trees.

Prevent rangers from setting controlled burns.

Answers

It is possible to avoid the spread of accidental wildfires in parks when we stop rangers from initiating a burn that is controlled. Option D

What is a wildfire?

The term wild fire refers to fires that burn uncontrollably. There are some factors that could lead to the beginning of wild fires. One of the several ways that we could have the emergence of a wild fire is if a fire is set up and then is left unattended.

The effects of this wild fire could be so devastating that large buildings as well as large habitats where organisms live could become permanently damaged from the raging of the wild fire and could now amount to a tremendous damage as well as the loss of biodiversity in the ecosystem.

Thus, It is possible to avoid the spread of accidental wildfires in parks when we stop rangers from initiating a burn that is controlled.

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Trucks carrying garbage to the town dump form a nearly steady procession on a country road, all traveling at 19.7 m/s in the same direction. Two trucks arrive at the dump every 3 min. A bicyclist is also traveling toward the dump, at 4.47 m/s.(a) With what frequency do the trucks pass the cyclist?

Answers

The truck passes the cyclist with a frequency of 8.59×10⁻³Hz.

What do you mean by frequency?

In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.

According to the question:

Using Doppler effects:

f' = (v+v₀/v-v₁)f

v₀ is the speed of the observer.

v₁ is the speed of the source.

v is the speed of sound in the medium.

Given:

v, speed of truck = 19.7m/s

f, frequency = 1/90Hz

v₀, speed of cyclist = 4.47m/s

v₁, speed of wave from a stationary source.

Putting in the equation:

f' = 8.59×10⁻³ Hz.

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A uniform magnetic field is directed along the x axis. For what orientation of a flat, rectangular coil is the flux through the rectangle a maximum? (a) It is a maximum in the x y plane. (b) It is a maximum in the x z plane. (c) It is a maximum in the y z plane. (d) The flux has the same nonzero value for all these orientations. (e) The flux is zero in all cases.

Answers

It is a maximum in the y z plane

Theoretically, magnetic field lines must traverse the coil's contained space in order for there to be magnetic flux through the coil. In contrast to the x y and x z planes, where the coils are located, the y z plane is where the magnetic field lines pass through.

How does magnetic flux work?

The entire magnetic field that traverses a particular area is measured by magnetic flux. It is a helpful tool for explaining how the magnetic force affects things inhabiting a certain area. The precise area selected will determine how magnetic flux is measured.

When the field is perpendicular to the coil's region, the flux is at its highest level. When the x axis is located in the plane of the loop and there is no magnetic field component perpendicular to the loop, the flux is zero.

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if blinded by an approaching motor vehicle at night, it is best to: stop dim your lights and continue at the same speed slow down and avoid looking directly into the lights of the approaching vehicle leave your lights on bright to offset the glare submit answer

Answers

If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.

What is a Vehicle?

This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.

In a situation whereby an individual is blinded  by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.

This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.

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A particle's location is measured and specified as being exactly at x = 0 , with zero uncertainty in the x direction. How does that location affect the uncertainty of its velocity component in the y direction? (a) It does not affect it. (b) It makes it infinite. (c) It makes it zero.

Answers

It does not affect the uncertainty of the velocity component in the y direction.

Any of a number of mathematical inequalities known as the uncertainty principle establishes a fundamental upper bound on the precision with which initial conditions can be used to forecast the values of some pairs of physical properties of a particle, such as location and momentum.

The measured and stated location of a particle is at x = 0 with zero uncertainty in the x direction.

According to the uncertainty principle, positional and velocity uncertainty are related along the same axis. The velocity component's x-directional component is infinitely uncertain due to the zero uncertainty in location along the x-axis, while the y-directional component is unaffected.

The correct option is (a).

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Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value
is 161.4 degrees Celcius.
The melting point of salicylic acid is known very well as 158.6 degrees Celcius.
What is Bubba's percent error?

Answers

Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value is 161.4 degrees Celsius. The melting point of salicylic acid is known very well as 158.6  degrees Celsius. Bubba's percent error will be 1.74 %

Percentage error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

estimated value of melting point = 161.4 °C

true value of melting point = 158.6 °C

percent error = ((true value - expected value) / expected value) * 100

                       = ((158.6 - 161.4 ) / 161.4 ) * 100

                       = 1.74 %

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The molar specific heat of a diatomic gas is measured at constant volume and found to be 29.1 J/mol .K. What are the types of energy that are contributing to the molar specific heat? (a) translation only (b) translation and rotation only (c) translation and vibration only (d) translation, rotation, and vibration

Answers

Answer:- b

Explanation:

The temperature of the diatomic atom's environment will vary the contributing kinetic energies for its heat capacity. At 60 K or below, the main contributor of energy is translational energy only. When the temperature rises up to about room temperature to 600 K, the contribution of rotational energy starts to be significant. When the temperature exceeds 3000 K, vibration energy is contributing to the heat capacity of a diatomic gas.

The formula for the specific heat capacity at constant volume is:

 where d is for degrees of freedom.

The translational motion contribute 3 degrees of freedom, meanwhile, the rotational and vibrational motion contributes 2 each for the degrees of freedom. Having 29.1 J/mol-K as the molar heat capacity at constant volume, the equation will be:

 

Having the degrees of freedom = 7 means that d.) translation, rotation, and the vibration is contributing.

Answer: B

S The intensity of a sound wave at a fixed distance from a speaker vibrating at a frequency f is I . (b) Calculate the intensity if the frequency is reduced to f / 2 and the displacement amplitude is doubled.

Answers

The intensity if the frequency is reduced from f to f / 2 and the displacement amplitude doubled is I.

What do you mean by frequency?

The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is stated. The period is the reciprocal of the frequency since it is the length of time for one cycle in a repeating occurrence. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).

I=P/4πr²

Given:

Initial frequency, f = f

Initial Intensity, I = I

Final Frequency, [tex]f^{'}=\frac{f}{2}[/tex]

We know that, The intensity of the speaker is,

[tex]I = \frac{1}{2}\rho \omega^{2}S_{max} ^{2}v[/tex]

Substitute the [tex]\omega[/tex] value in the above equation,

[tex]I = \frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v\;\;\;\;-----equation(1)[/tex]

Therefore, Final intensity of the speaker is,

[tex]I^{'} = \frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v\;\;\;\;-----equation(2)[/tex]

By dividing the equation (1) and (2), We get

[tex]\frac{I}{I^{'}} = \frac{\frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v}{\frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v}[/tex]

By taking constant parameters in to account, We get,

[tex]\frac{I}{I^{'}} = \frac{(f)^{2}(S_{max}) ^{2}}{(f^{'} )^{2}(S_{max} )^{2}}[/tex]

By solving the above equation, We get

[tex]\frac{I}{I^{'}} = \frac{(f)^{2}}{4(f^{'} )^{2}}[/tex]

Substitute the final intensity value in the above equation,

[tex]I^{'} = I[\frac{4(\frac{f}{2})^{2}}{f^{2} }][/tex]

By solving the above equation, We get,

[tex]I^{'} = I[/tex]

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How long would it take a 1000W heater to melt 1.00kg of ice at -20.0°C, assuming all the energy from the heater is absorbed by the ice? (a) 4.18 s(b) 41.8 s (c) 5.55 min (d) 6.25min(e) 38.4min

Answers

Answer:

Heat for -20 to zero = .48 * 1000 = 480 calories

Heat to melt ice = 1000 * 79.7 = 79700 calories

Total calories required = 80,200 calories

80,200 cal * 4.19 J/cal = 336,000 J

336000 J / 1000 J/sec = 336 sec

336 sec / 60 sec/min = 5.6 min

(c - 5.55 min)

The highest speed achieved by a standard non racing sports car is 3.60 x 10² km/h. Assuming that the car accelerates at a constant rate to reach this maximum speed for 25.0 s and covers a distance of 1.50 km while accelerating, what was the initial velocity of the car?

Answers

The car has a constant acceleration of 1.95m/s2 and reaches a top speed of 41.0m/s. The boat has a constant acceleration of 6.50m/s2 .

What is acceleration ?

When it comes to mechanics, acceleration refers to how quickly an object's velocity changes over time. Acceleration is a vector quantity (in that they have magnitude and direction). The direction of the net force acting on an item determines its acceleration.

According to Newton's Second Law, an object's acceleration is a sum of two factors:

The size of the net balance of all external forces acting on that thing is directly proportional to the net resultant force; the magnitude of the object's mass, depending on the materials from which it was created, is inversely related to the mass.

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For most of history, the lack of observable stellar parallax was interpreted to mean that.

Answers

Answer:For most of history, the lack of observable stellar parallax was interpreted to mean that: Earth is stationary at the center of the Universe.

Explanation:

Which equation is perpendicular to the line
(1901
y = 3 and passes through the point (- 1, 3).
a. x = 3
b. y = 3
c. y = -1
d. X = -1

Answers

The equation perpendicular to the line is y=3.

The slope of the line [tex]$3 x+y=3$[/tex] is [tex]$m=-3$[/tex]

Hence slope of the perpendicular line is [tex]$\mathrm{m}^{\prime}=\frac{1}{3}$[/tex]

Therefore the equation of a perpendicular line is

Therefore the equation of a perpendicular line is

[tex]$(\mathrm{y}+1)=\frac{1}{3}(\mathrm{x}-3) $[/tex]

[tex](y+3)=\frac{1}{3}(x-1)[/tex]

Switch sides

[tex]\frac{1}{3}(x-1)=(y+3)[/tex]

[tex]$\frac{1}{3}(x-1)=y+3$[/tex]

Multiply both sides by 3

[tex]$3 \cdot \frac{1}{3}(x-1)=3 y+3 \cdot 3$[/tex]

Simplify

[tex]$x-1=3 y+9$[/tex]

Add 1 to both sides

[tex]$$x-1+1=3 y+9+1$$[/tex]

Simplify

[tex]$$x=3 y+10$$[/tex]

y= 3.33 (Approx 3)

The two different lines that cross each other at a 90° angle are called perpendicular lines. Have you observed any similarities between the walls' intersecting corners, such as the letter "L"? They are parallel lines, which are straight lines that cross each other at the proper angle.

If two lines cross at a 90° angle, we say that they are perpendicular to one another.

the vertex's matching angle is a right angle. All crossing lines are not necessarily perpendicular to one another, but perpendicular lines always cross each other. Perpendicular lines have two key characteristics.

In every case, perpendicular lines cross or intersect.

Any two perpendicular lines will always intersect at an angle of 90 degrees.

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Review. A proton is at rest at the plane boundary of a region containing a uniform magnetic field B (Fig. P29.59). An alpha particle moving horizontally makes a head-on elastic collision with the proton. Immediately after the collision, both particles enter the magnetic field, moving perpendicular to the direction of the field. The radius of the proton's trajectory is R . The mass of the alpha particle is four times that of the proton, and its charge is twice that of the proton. Find the radius of the alpha particle's trajectory.

Answers

The radius of the alpha particle's trajectory is [tex]r_{\alpha } =\frac{3}{4} (R(proton))[/tex].

What is trajectory?

The journey through space and time taken by a mass-moving object is referred to as its trajectory or flight path. Since a trajectory is determined by Hamiltonian mechanics using canonical coordinates, a full trajectory in classical mechanics is defined by position and momentum simultaneously.

A satellite or a missile could represent the mass. For example, a planet, asteroid, or comet moves around a major body in a path called an orbit.

A projectile's trajectory, such as that of a ball or rock thrown, is a well-known example of a trajectory. In a greatly simplified model, an object only moves when it experiences a constant gravitational force field.

Calculations:

Since, the collision is elastic:

Therefore, momentum will be conserved.

Which means:  [tex]m_{p}.v_{p} + m_{\alpha}.v_{\alpha } = m_{\alpha } . v_{0} +m_{p} .v_{po}[/tex]

[tex]m_{p}.v_{p} + m_{\alpha}.v_{\alpha } = m_{\alpha } . v_{0} ......(i)[/tex]

Similarly, for elastic collision:

Additionally conserved is kinetic energy:[tex]KE_{f}[/tex][tex]=KE_{I}[/tex]

                                       =1/2 [tex]m_{p}[/tex][tex]v_{p} ^{2}[/tex]+[tex]1/2 m_{\alpha }.v_{\alpha } ^{2}[/tex]=[tex]1/2m_{\alpha } v_{0} ^{2}[/tex]

For head on collision: ([tex]v_{0} -v_{p0}[/tex])=[tex](v_{\alpha } - v_{p} )[/tex]

                                     [tex]v_{\alpha } +v^{0} =v_{p}[/tex].......(ii)

and,[tex]m_{\alpha } =4m_{p}[/tex].....(iii)

therefore equation(i) becomes.

                     [tex]5v_{\alpha } =3v_{0} \\v_{\alpha } =\frac{3}{5} v_{0} \\[/tex].......(iv)

From equation (ii) and (iv)   [tex]v_{p} = \frac{3}{5} v_{0} +v_{0} =\frac{8}{5} v_{0}[/tex].......(v)

From equation (iv) and (v)    [tex]\frac{v_{p} }{v_{\alpha } } =\frac{8}{3}[/tex]

Since, [tex]r=\frac{mv}{qB}[/tex]

R(proton)=[tex]\frac{m_{p} v_{p} }{eB}[/tex]

[tex]r_{\alpha } =\frac{3}{4} (\frac{m_{p}v_{p} }{eB } )[/tex]

[tex]r_{\alpha } =\frac{3}{4} (R(proton))[/tex]

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Q|C Spherical waves of wavelength 45.0cm propagate outward from a point source. (b) Explain how the amplitude at a distance of 240cm compares with the amplitude at a distance of 60.0cm.

Answers

The difference between the amplitude at a distance of 60.0 cm and 240 cm is  I240 = 16×I60

           A240=4×I60

Δ∅240=4.Δ∅60

We are given distance of the center of the source for two waves:

D1=240 cm

D2=60.0 cm

b) Calculating how their amplitude compares:

[tex]A_{240} =\sqrt{\frac{I_{240} }{I_{60} } } .A_{60}[/tex]

[tex]=\sqrt{16} .A_{60}[/tex]

[tex]A_{240} = 4. A_{60}[/tex]

How can you determine a wave's phase?

The period, or length of each cycle, is determined by dividing the frequency by 1, so 1/100 corresponds to a period of 0.01 seconds. The phase shift equation is given by ps = 360 * td / p, where td is the time interval between waves, p is the wave period, and ps is the phase shift in degrees.

Phase: The "Phase" of a waveform refers to the location of the moving particle and is expressed in "Radians or degrees."

Phase difference, also known as "Phase angle," is the amount of time that one wave precedes or follows another.

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Because most particles fired at metal foil passed straight through, rutherford concluded that.

Answers

Answer:

Rutherford deduced that atoms were mostly empty space

Explanation:

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