what is the potential difference between yi =−7cm and yf =7cm in the uniform electric field e⃗ =(20,000i^−75,000j^)v/m?

Answers

Answer 1

The potential difference between the points at yi = -7cm and yf = 7cm in the given electric field is 1,050,000 V.

The electric field is given as E⃗ = (20,000i^ - 75,000j^) V/m. This means that the electric field is only in the y-direction, and its magnitude is constant throughout.

To find the potential difference between two points in the electric field, we can use the following formula:

ΔV = -∫E⃗ · dl⃗

where ΔV is the potential difference, E⃗ is the electric field, and dl⃗ is an infinitesimal displacement along the path between the two points. The negative sign arises because the electric field is acting in the opposite direction to the direction of motion along the path.

In this case, we can assume a path that moves from the point at yi = -7cm to the point at yf = 7cm, both of which lie on the y-axis. Since the electric field is only in the y-direction, we can assume that the path is also along the y-axis. Therefore, we can simplify the formula to:

ΔV = -∫E dy

where the integral is taken from yi = -7cm to yf = 7cm.

Substituting the electric field E⃗ and integrating, we get:

ΔV = -∫E dy = -∫(-75,000) dy (since the y-component of the electric field is -75,000 V/m)

ΔV = -[-75,000y]yi=-7cm to yf=7cm

ΔV = -[-75,000(7cm - (-7cm))] = 1,050,000 V

Therefore, the potential difference between the points at yi = -7cm and yf = 7cm in the given electric field is 1,050,000 V.

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Related Questions

Show the molecular formula and electron structure of the simplest compound that forms with only carbon and hydrogen atoms.

Answers

The simplest compound of hydrocarbon is methane

The formula is CH_4It belongs to alkane group and has single bonds.

The electron structure attached

Show the molecular formula and electron structure of the simplest compound that forms with only carbon

in situ quantification of the active sites turnover frequency and stability of ni-fe oxy hydrooxide for the oxygen evolution reaction

Answers

The intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).

How does turnover frequency and stability of ni-fe oxy hydroxide for the oxygen evolution reaction?

Understanding the intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).

The understanding of Ni-Fe (oxy)hydroxides' electro catalytic activity and stability is hampered by the lack of efficient methods for measuring the Fe active site number and the intrinsic turnover frequency per active Fe site (TOFFe), despite the fact that Fe has been proposed as one of the most active noble-metal-free electro catalysts for the alkaline oxygen evolution reaction (OER).

The direct in situ quantification of the electrochemically active Fe site number and associated TOFFe values of Ni-Fe (oxy)hydroxides using previously unstudied Fe2+/3+ redox electrochemistry in alkaline solutions is described in this article.

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When you listen to the radio, watch TV, or cook food in a microwave, you are making use of properties of electromagnetic waves. Which statement about electromagnetic waves is false?

A. White light is the absence of all color.
B. Higher-frequency electromagnetic waves have more energy.
C. The sun radiates several different types of electromagnetic energy.
D. The frequency of an electromagnetic wave is related to its wavelength.

Answers

Answer:

A. White light is the absence of all color.

Explanation:

It is false that white light is the absence of all color. In fact, white light is the presence of all colors in the spectrum.

Electromagnetic waves are waves that do not require any material medium for propagation. It is the interaction of electric and magnetic fields.

The higher frequency electromagnetic waves like the gamma-rays and x-rays have more energy. The sun furnishes the universe with electromagnetic energy. The higher the wavelength, the lesser the energy of the electromagnetic radiation.

What is the Force in Newtons exerted by brick with a mass of 0.5 kg and an Acceleration of 52m/s2?

Answers

F= a*m
F= 0.5 kg * 52m/s^2
F=26kgm/s^2 or 26N

If a building requires a handicap lift in the lobby of a building, who is responsible for paying for the installation and maintenance of the lift...?

Answers

The owner of the building is primarily responsible for paying for the installation and maintenance of the handicap lift.

What is a handicap lift?

A handicap lift in a building is a special purpose lift which is designed specifically for use by those who are handicapped.

Since handicapped individuals are not able to use all or parts of their body effectively building designs must take into cognizance the needs of the handicapped.

For a building in which a handicap is to live, a handicap lift is necessary in order to enable the handicapped individual to be able to freely move around, in and out of the building.

If a building requires a handicap lift in the lobby of a building, the building owner is primarily responsible for paying for the installation and maintenance of the lift.

In conclusion, a handicap lift is essential in a building in which a handicapped individual lives.

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how do you get derived units from derived quantities

Answers

Answer:

A derived quantities is terms of the 7 base quantities via a system of quantity equations which are called SI derived units.

Explanation: there you go:)

on a hertzsprung-russell diagram describing the stars in a young cluster, in which position would you expect to find the t tauri stars?

Answers

The Hertzsprung-Russell diagram (HR diagram) is a tool used to study stars and their properties. It plots the luminosity (brightness) of stars against their temperature. Young clusters are groups of stars that are relatively new and have not yet undergone significant changes.

Now, onto the t Tauri stars. These are a type of pre-main sequence star, which means they are still in the process of forming and contracting. They are located in the lower-right corner of the HR diagram. This area is known as the T Tauri region.

The reason t Tauri stars are found in this region is that they are not yet generating energy through nuclear fusion in their cores. Instead, they are still contracting and heating up as a result of gravitational collapse. As a result, they are relatively cool and dim, with surface temperatures ranging from about 3,000 to 4,500 Kelvin.

In summary, if we were to plot the stars in a young cluster on an HR diagram, we would expect to find t Tauri stars in the lower-right corner of the diagram, in the T Tauri region.

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Why is the use of carbon- 14 dating limited?​

Answers

Answer:

because carbon 14 has only a short half life, rather than other elements with longer half lives.

Explanation:

✨science✨

What is the kinetic Energy of a 350 kg object that is moving with a speed of 5 m/s?

What is the kinetic energy of a 65 kg object that is moving with a speed of 20 m/s?

I just need the work not the answers, sorry if its too much.​

Answers

Answer:

Explanation:

4375J

A small water droplet in a mist of air is approximated as being a sphere of diameter 1.25 mil. Calculate the terminal velocity as it falls through still air to the ground.

Answers

The terminal velocity as it falls through still air is 4.65154 in/s.

The diameter of small water droplet is 1.25 mil= 1.25×0.0254×10^-3 m

                                                                            = 3.175 × 10^-5 m

Now the viscosity of still air is η = 1.83× 10⁻⁵ Pa

 So the formula for drag force is:

                Fd = 6πηrv

  where,  v is the velocity.

Now to attain terminal velocity acceleration must be zero.

            →  W = Fd

                ρVg = 6πrηv

                ρ × 4/3 πr³×g = 6πrηv

                           v = 2/9 × ρgr³/ η

                           v =  2/9 × 10³×9.81×(3.175×10^-3) / 18.6×10^-6

                           v = 0.1181  m/s

                           v = 4.65154 in/s

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Find Vy and Vx when the resultant vector is 145m/s and the angle is 55.

Answers

In order to find the horizontal and vertical components of the given vector, we can use the formulas below:

\(\begin{gathered} V_x=V\cdot\cos\theta\\ \\ V_y=V\cdot\sin\theta \end{gathered}\)

So, if the magnitude of the resultant vector is 145 m/s and the angle is 55°, we have:

\(\begin{gathered} V_x=145\cdot\cos55°\\ \\ V_x=83.17\text{ m/s}\\ \\ \\ \\ V_y=145\cdot\sin55°\\ \\ V_y=118.78\text{ m/s} \end{gathered}\)

if the wind over the surface ocean is blowing to the north, in the ocean below, in what direction is the flow at the bottom of the ekman spiral?

Answers

In the ocean below the surface, the flow at the bottom of the Ekman spiral is generally in the opposite direction to the wind direction. Therefore, if the wind over the surface ocean is blowing to the north, the flow at the bottom of the Ekman spiral would be generally to the south.

The Ekman spiral describes the phenomenon of how wind-driven surface currents in the ocean gradually turn with depth due to the influence of the Coriolis effect. As the wind blows across the ocean surface, it transfers some of its momentum to the layer of water just below, causing it to move in the direction of the wind but slightly to the right in the Northern Hemisphere (due to the Coriolis effect). This process continues with each successive layer of water, resulting in a spiral pattern of flow.

At the bottom of the Ekman spiral, the cumulative effect of the wind-driven surface currents leads to a net flow in the opposite direction to the wind, which is generally to the south when the wind is blowing to the north. However, it's important to note that other factors such as oceanic circulation patterns, bathymetry, and coastal effects can also influence the direction of flow at the bottom of the Ekman spiral.

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An atom of element X has one more
shell of electrons than an atom of
calcium, but it has one less valence
electron than calcium. Which element
is element X?

Answers

Answer:

Rubidium or Rb

Explanation:

Use the periodic table, the period numbers are number of shells while the group numbers are numbers of valence electrons

.
\(25 {?}^{?} \times \frac{?}{?} \)

Answers

Answer:

what is your exact question.

what are u asking exactly ?

Bill drives west at 20\, \dfrac{\text m}{\text s}20 s m ​ 20, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, then slows to a stop at the red light. A graph of his velocity over time is shown below, where eastward is the positive velocity direction.

Answers

Answer:

This

Explanation:

Khan academy answer

Bill drives west at 20\, \dfrac{\text m}{\text s}20 s m 20, start fraction, start text, m, end text,

A force of 200N acts between two objects at a certain distance apart .the value of the force when the distance is halved is?

Answers

Answer:

800N is the answer

Explanation:

hope it helps

The force between the objects is 200 N and when the distance between the objects is halved then the force between them will be equal to 800 N.

What is Force?

A force in physics is an input that has the power to change an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe forces.

Being such a vector quantity, a force does have magnitude and direction. The SI unit metric newton is used to measure it (N). The letter F stands for force.

According to Newton's second law's original formulation, an object's net force is equal to the speed that its momentum is changing over time.

As per the given information in the question,

Force, F = 200 N

F1 = G × m₁m₂/ r²

The final force F' = G × m₁m₂/ (r/2)²

= 4G × m₁m₂/ r²

= 4F

So, when the distance between objects is halved, then the force between them increases to 4 times.

So, the force will be,

4F = 4 × 200

= 800 N.

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which country is focused on ranking social class according to ascribed status?

Answers

The Indian caste system is one of the most rigid and long-lasting social systems in the world. This is a social framework that assigns people a caste based on their birth and prohibits mobility across castes.

What is the connection between assigned status and social class?

Ascribed status is a phrase used in sociology that refers to the social standing of a person who is assigned at birth or assumed unwillingly later in life and is assigned at birth or assumed involuntarily later in life. A person's status is a position that is neither earned nor chosen for them.

Apart from innate distinctions, individuals also discriminate based on their position, power, money, and other factors. It's also called social stratification or social inequality.

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A stationary block of mass 35 Kg is suspended on a string.What is the tension in the string ?( Neglect the mass of the string)

Answers

Answer:

Tstring = 343.35 [N]

Explanation:

Since the block is in equilibrium, we can say that the sum of the forces on the Y-axis or vertical is equal to zero.

∑Fy = 0

\(T_{string}-W=0\)

where:

Tstring = tension of the string [N]

W = weight of the block [N]

And the weight can be calculated multiplying the mass of the block by the gravity acceleration.

Now replacing:

\(T_{string}=m*g\\T_{string}=35*9.81\\T_{string}=343.35[N]\)

How far could a force of 3N pull a wooden block before transferring 12J of energy?

Answers

The distance which a force of 3N will pull a wooden block before transferring 12J of energy is 4m.

What is Force?

This is referred to as an influence that can change the motion of an object and the unit is Newton.

It has a relationship with distance and work which can be seen below:

Work = Force × distance

12J = 3N × d

d = 12/3 = 4m.

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Predict how your observations would change if you used a beaker with the same mass of lower temperature water.​

Predict how your observations would change if you used a beaker with the same mass of lower temperature

Answers

The transfer of warmth (heat) from one item to another is known as heat conduction. Therefore, we can witness heat or thermal conduction when two things with differing temperatures come into touch.

Thus, The heat transfers from the hotter (the cup) to the colder (our hands) object when we contact the hot cup. When we added hot water to the cup that was at normal temperature, thermal conduction also took place.

The object's temperature is actually a measurement of how quickly its atoms are moving. The total energy produced by the atoms' vibrations is measured by the heat.

As a result, the atoms inside it begin to travel more quickly, which inevitably raises the likelihood that they will collide and conduction. It also relies on the density of the material we are working with how much they will clash.

Thus, The transfer of warmth (heat) from one item to another is known as heat conduction. Therefore, we can witness heat or thermal conduction when two things with differing temperatures come into touch.

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you see a displayed diver-down flag while boating. if possible, how far away must you stay from the flag?

Answers

If you see a displayed diver-down flag while boating, it is necessary to maintain a certain distance from the flag for safety reasons. The specific distance may vary depending on local regulations and circumstances, but it is generally recommended to stay at least 100 feet away from the flag.

A diver-down flag is used to indicate the presence of divers in the water. Its purpose is to alert boaters to the potential hazards and to ensure the safety of the divers. The exact distance you must stay away from the flag may be specified by local laws or regulations, so it is important to familiarize yourself with the rules of the area you are boating in.

In many places, a common guideline is to stay at least 100 feet away from the diver-down flag. This distance allows for a safe buffer zone to prevent any accidental collisions or disturbances to the divers. However, it's crucial to check and adhere to the specific regulations in your boating location, as they may vary and could require a different distance to be maintained. Prioritizing safety and respecting the presence of divers is essential to avoid any accidents or harm to both boaters and divers.

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If a ball is thrown from a tall building, how tall is the building if it takes 6s for the ball to land?

Answers

Answer:

the answer is 352.8m

Explanation:

Since the gravitational constant is denoted as g

\(g = 9.8 \: \frac{m}{ {s}^{2} }\)

and the ball needed 6 seconds to land, so we can calculate the height of the building as:

\(h = 9.8 \: \frac{m}{ {s}^{2} } \times {(6s)}^{2} = 9.8 \: \frac{m}{ {s}^{2} } \times 36 {s}^{2} = 352.8m\)

A 2300-kg car slows down at a rate of 3.0 m/s2 when approaching a stop sign. What is the magnitude of the net force causing it to slow down?

Answers

The magnitude of the net force causing the 2300kg car to slow down is 6900N

HOW TO CALCULATE FORCE:

The net force applied on a moving object can be calculated by multiplying the mass of the object by its acceleration. That is;

Force (N) = mass (kg) × acceleration (m/s²)

According to this question, a 2300-kg car slows down at a rate of 3.0 m/s2 when approaching a stop sign. The net force causing the car to stop can be calculated as follows:

F = 2300kg × 3m/s²

F = 6900N

Therefore, the magnitude of the net force causing the 2300kg car to slow down is 6900N.

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WILL GIVE BRAINLIST TO THE CORRECT ANSWER!

Read the two passages.

Excerpt from The Gettysburg Address, 1863

By Abraham Lincoln

Four score and seven years ago, our fathers brought forth upon this continent a new nation: conceived in liberty, and dedicated to the proposition that all men are created equal.… Now we are engaged in a great civil war…[and many have died]. It is for us the living…to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us ...that we here highly resolve that these dead shall not have died in vain...that this nation, under God, shall have a new birth of freedom...and that government of the people...by the people...for the people...shall not perish from this earth.

Excerpt from John F. Kennedy’s Inaugural Address, 1961

By John F. Kennedy

In the long history of the world, only a few generations have been granted the role of defending freedom in its hour of maximum danger; I do not shrink from this responsibility.… I welcome it. I do not believe that any of us would exchange places with any other people or any other generation. The energy, the faith, the devotion which we bring to this endeavor will light our country and all who serve it…and the glow from that fire can truly light the world. And so, my fellow Americans…ask not what your country can do for you…ask what you can do for your country. My fellow citizens of the world…ask not what America will do for you, but what together we can do for the Freedom of Man.

According to the supporting details, what do the speeches by Lincoln and Kennedy have in common?

A. Both speeches mention that the presidents do not welcome the role of defending freedom.

B. Both speeches express they do not want those who have died during a war to have died in vain.

C. Both speeches indicate a desire to motivate and unite Americans in order to preserve freedom.

D. Both speeches pose a question for each American to ask themselves.

Answers

Answer:

the best answer would be c

Explanation:

Answer: C. Both speeches indicate a desire to motivate and unite Americans in order to preserve freedom

Explanation:

A water-balloon launcher with a mass of 1.75 kg is suspended on a wire. It fires a 1.25 kg balloon to the east at a velocity of 12.0 m/s. What is the resulting velocity of the launcher if the net force on the launcher is equal to the reaction force? O A. 6.1 m/s east B. 16.8 m/s west C. 7.6 m/s west D. 8.6 m/s west​

Answers

Answer:

8.6 to west

Explanation:

The initial momentum of the system is given by the sum of the momentum of the launcher and the momentum of the balloon. The correct answer is option C. 7.6 m/s west.

To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.

The momentum of an object is calculated by multiplying its mass by its velocity.

Initial momentum = (mass of launcher × velocity of launcher) + (mass of balloon × velocity of balloon)

Let's substitute the given values into the equation:

Initial momentum:

\((1.75 kg * 0 m/s) + (1.25 kg * 12.0 m/s)\)

Initial momentum = 15 kg·m/s

Since the net force on the launcher is equal to the reaction force, we can assume no external forces act on the system. Therefore, the total momentum before firing the balloon is equal to the total momentum after firing the balloon.

Final momentum = (mass of launcher + mass of balloon) × final velocity of the launcher

Let's solve for the final velocity of the launcher:

Final momentum:

\((1.75 kg + 1.25 kg)\) × Final velocity of the launcher

15 kg·m/s = 3 kg × final velocity of the launcher

Dividing both sides of the equation by 3 kg gives us:

The final velocity of the launcher = 15 kg·m/s / 3 kg

The final velocity of the launcher = 5 m/s

Since the initial velocity of the balloon is to the east, the final velocity of the launcher will be to the west. Therefore, the correct answer is option C. 7.6 m/s west.

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what is $12.7\ge s-5.3$ .

Answers

The solution of expression $12.7\ge s-5.3$ is $s \leq 18$.

The expression $12.7\ge s-5.3$ is an inequality, which means that it expresses a range of values for the variable $s$. The symbol $\ge$ means "greater than or equal to," and in this context it indicates that $12.7$ is greater than or equal to $s-5.3$.

To solve for $s$, we can start by adding $5.3$ to both sides of the inequality:

\begin{align*}

12.7 &\ge s-5.3 \

12.7+5.3 &\ge s-5.3+5.3 \

18 &\ge s

\end{align*}

So the solution is $s \leq 18$. This means that any value of $s$ that is less than or equal to $18$ will satisfy the inequality. For example, $s=15$ would satisfy the inequality, because $12.7 \ge 15-5.3$. However, $s=20$ would not satisfy the inequality, because $12.7 \ngeq 20-5.3$.

What are the variables?

A variable is a symbol or letter that represents a value that can vary or change in a given context or problem. Variables are used to write mathematical expressions, equations, and functions.

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Complete question is: $12.7\ge s-5.3$ is $s \leq 18$.

Calculate the potential at the centre of a square of side √4.5 m which carries at its
four corners and charges of + 5 x 10° C, 2 x 10°C, -5 x 10° C and - 7 x 10°C
respectively

Answers

Thus, the total potential is then V_total = \(-1.2 * 10^9V\)


How to solve

The potential at a point due to a charge is given by V = kQ/r, where k is Coulomb's constant (~\(9x10^9 Nm^2/C^2\)), Q is the charge, and r is the distance from the charge.

The total potential at the center of the square is the sum of the potentials due to each charge.

The distance of each charge to the center is half the diagonal of the square, which is \(\sqrt2 * side/2 = \sqrt2 * \sqrt4.5/2 = 1.5m.\)

The total potential is then V_total

= \(k * [(510^8/1.5) + (210^8/1.5) - (510^8/1.5) - (710^8/1.5)] = -2 * k * 10^8 / 1.5 \\= -1.2 x 10^9 V.\)

Thus, the total potential is then V_total = \(-1.2 * 10^9V\)

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true or false Oxygen atoms bond together, but this is not because of an atomic force.”

Answers

Answer:

this is false not correct no FALSE

1. What is the wave speed of a wave that has a frequency of 100 Hz and a wavelength of 0.30 m?

30 m/s


2. What is the wave speed of a wave that has a frequency of 50 Hz and a wavelength of 0.10 m?

0.772m


3. What is the frequency of a wave that has a wave speed of 20 m/s and a wavelength of 0.50 m?

40 Hz


4. What is the frequency of a wave that has a wave speed of 80 m/s and a wavelength of 0.20 m?




5. What is the frequency of a wave that has a wave speed of 120 m/s and a wavelength of 0.40 m?




6. What is the wavelength of a sound wave that has a speed of 340 m/s and a frequency of 440 Hz?




7. What is the wavelength of a sound wave that has a speed of 340 m/s and a frequency of 880 Hz?




8. What is the wavelength of a sound wave that has a speed of 250 m/s and a frequency of 400 Hz?




9. What is the wave speed of a wave that has a frequency of 50 Hz and a wavelength of 2.0 m?




10. What is the wave speed of a wave that has a frequency of 100 Hz and a wavelength of 0.50 m?

Answers

Answer:

1. v = 30 m/s

2. v = 5 m/s

3. f = 40 Hz

4. f = 400 Hz

5. f = 300 Hz

6. λ = 0.772 m

7. λ = 0.386 m

8. λ = 0.625 m

9. v = 100 m/s

10. v = 50 m/s

Explanation:

The relationship between frequency, wavelength, and speed of a wave is given by the following formula:

\(v = f\lambda\)

where,

v = speed of wave

f = frequency of wave

λ = wavelength

1.

f = 100 Hz

λ = 0.3 m

Therefore,

v = (100 Hz)(0.3 m)

v = 30 m/s

2.

f = 50 Hz

λ = 0.1 m

v = (50 Hz)(0.1 m)

v = 5 m/s

3.

v = 20 m/s

λ = 0.5 m

\(f = \frac{v}{\lambda} = \frac{20\ m/s}{0.5\ m}\)

f = 40 Hz

4.

v = 80 m/s

λ = 0.2 m

\(f = \frac{v}{\lambda}=\frac{80\ m/s}{0.2\ m}\)

f = 400 Hz

5.

v = 120 m/s

λ = 0.4 m

\(f = \frac{v}{\lambda}=\frac{120\ m/s}{0.4\ m}\)

f = 300 Hz

6.

v = 340 m/s

f = 440 Hz

\(\lambda = \frac{v}{f}=\frac{340\ m/s}{440\ Hz}\\\)

λ = 0.772 m

7.

v = 340 m/s

f = 880 Hz

\(\lambda = \frac{v}{f}=\frac{340\ m/s}{880\ Hz}\\\)

λ = 0.386 m

8.

v = 250 m/s

f = 400 Hz

\(\lambda = \frac{v}{f}=\frac{250\ m/s}{400\ Hz}\\\)

λ = 0.625 m

9.

f = 50 Hz

λ = 2 m

v = (50 Hz)(2 m)

v = 100 m/s

10.

f = 100 Hz

λ = 0.5 m

v = (100 Hz)(0.5 m)

v = 50 m/s

Answer:

it B

Explanation:

I KNOW IT

how fast must you be approaching a red traffic light ( λ = 675 nm ) for it to appear yellow ( λ = 575 nm )? express your answer in terms of the speed of light.

Answers

So, to observe the red traffic light as yellow, the observer must approach the light with a speed of 0.148 times the speed of light.

When the observer approaches the red traffic light with a speed, the light appears shifted towards the blue end of the spectrum. The apparent frequency and wavelength shift is calculated using the Doppler effect equation.

The Doppler shift is given by the relation f′= f (v+vO)/c

where, f' is the observed frequency, f is the frequency of the wave, v is the speed of the observer, v O is the speed of the source and c is the speed of the wave.

For the red traffic light,

f= c/λ = 4.44 × 10^14 Hzλ

= 675 nm

For the yellow traffic light,

f = c/λ

= 5.22 × 10^14 Hzλ

= 575 nm

As we know that the light appears yellow when the red light shifts 575 nm.

Therefore, the observer should be approaching the light with a speed given by the relation as,

∆f/f = v/c⇒ ∆λ/λ

= v/c⇒ v

= c (∆λ/λ)

= c [(λ_0 - λ)/λ_0 ]

Where,λ is the wavelength of the shifted light (λ = 575 nm),λ0 is the wavelength of the unshifted light (λ0 = 675 nm)

Therefore,

v = c [(675 - 575)/675]⇒ v

= 0.148c

So, the observer must approach the red traffic light at a speed of 0.148 times the speed of light to observe it as yellow.

An observer, when approaching a red traffic light, experiences a shift in the light's wavelength towards the blue end of the spectrum. This apparent frequency and wavelength shift is given by the Doppler effect equation.

The Doppler shift can be expressed using the relation,

f′= f (v+vO)/c

where, f' is the observed frequency, f is the frequency of the wave, v is the speed of the observer,v O is the speed of the source and c is the speed of the wave.

The frequency and wavelength of the red and yellow traffic lights are,

f= c/λ

= 4.44 × 10^14 Hz,

λ = 675 nm and

f = c/λ

= 5.22 × 10^14 Hz,

λ = 575 nm.

Since we know that the light appears yellow when the red light shifts by 575 nm, the observer must be approaching the light with a velocity given by the following relation:

∆f/f = v/c⇒ ∆λ/λ

= v/c⇒ v

= c (∆λ/λ_0 ) where λ_0 is the wavelength of the unshifted light (λ_0 = 675 nm)

Therefore,

v = c [(675 - 575)/675]⇒ v

= 0.148c

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