Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 35: Problem 83

In a high-speed football game, a running back traveling at \(55.0 \%\) of the speed of light relative to the field throws the ball to a receiver running in the same direction at \(65.0 \%\) of the speed of light relative to the field. The speed of the ball relative to the running back is \(80.0 \%\) of the speed of light. a) How fast does the receiver perceive the speed of the ball to be? b) If the running back shines a flashlight at the receiver, how fast will the photons appear to be traveling to the receiver?

Short Answer

Expert verified
Answer: The receiver perceives the speed of the ball to be 95.39% of the speed of light, and the speed of the photons from the flashlight as perceived by the receiver is 100% of the speed of light (c).

Step by step solution

01

Calculate the velocities in terms of the speed of light

First, convert the given percentages to decimals and multiply by the speed of light (c) to find the velocities of the running back, receiver, and ball relative to each other: Running back: \(0.55c\) Receiver: \(0.65c\) Ball relative to the running back: \(0.80c\)
02

Apply the relativistic velocity addition formula

Use the relativistic velocity addition formula to find the perceived speed of the ball by the receiver: \(v_{BR} = \frac{v_{B} + v_{R}}{1 + \frac{v_{B}v_{R}}{c^2}}\) Here \(v_{BR}\) is the velocity of the ball relative to the receiver, \(v_{B}\) is the velocity of the ball relative to the running back, and \(v_{R}\) is the velocity of the receiver relative to the field.
03

Plug in the values and solve for \(v_{BR}\)

Insert the known velocities into the equation: \(v_{BR} = \frac{0.80c + 0.65c}{1 + \frac{(0.80c)(0.65c)}{c^2}}\) Simplify the equation and solve for \(v_{BR}\): \(v_{BR} = \frac{1.45c}{1 + 0.52}\) \(v_{BR} = \frac{1.45c}{1.52}\) \(v_{BR} = 0.9539c\) So, the receiver perceives the speed of the ball to be \(95.39 \%\) of the speed of light. This solves part (a) of the exercise.
04

Determine the speed of the photons from the flashlight

Since photons travel at the speed of light, they have the maximum possible speed in the universe. No matter the speed of the source or the observer, photons will always appear to travel at the speed of light. Therefore, for part (b), the speed of the photons from the flashlight as perceived by the receiver is \(c\) or \(100 \%\) of the speed of light.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which quantity is invariant-that is, has the same value-in all reference frames? a) time interval, \(\Delta t\) d) space-time interval, b) space interval, \(\Delta x\) \(c^{2}(\Delta t)^{2}-(\Delta x)^{2}\) c) velocity, \(v\)

You shouldn't invoke time dilation due to your relative motion with respect to the rest of the world as an excuse for being late to class. While it is true that relative to those at rest in the classroom, your time while you are in motion runs more slowly, the difference is negligible. Suppose over a weekend you drove from your college in the Midwest to New York City and back, a round- trip of \(2200 . \mathrm{mi}\), driving for \(20.0 \mathrm{~h}\) in each direction. By what amount, at most, would your watch differ from your professor's watch?

If a muon is moving at \(90.0 \%\) of the speed of light, how does its measured lifetime compare to its lifetime of \(2.2 \cdot 10^{-6} \mathrm{~s}\) when it is in the rest frame of a laboratory?

Use relativistic velocity addition to reconfirm that the speed of light with respect to any inertial reference frame is \(c .\) Assume one-dimensional motion along a common \(x\) -axis.

Three groups of experimenters measure the average decay time for a specific type of radioactive particle. Group 1 accelerates the particles to \(0.5 c,\) moving from left to right, and then measures the decay time in the beam, obtaining a result of 20 ms. Group 2 accelerates the particles to \(-0.5 c,\) from right to left, and then measures the decay time in the beam. Group 3 keeps the particles at rest in a container and measures their decay time. Which of the following is true about these measurements? a) Group 2 measures a decay time of \(20 \mathrm{~ms}\). b) Group 2 measures a decay time less than \(20 \mathrm{~ms}\). c) Group 3 measures a decay time of \(20 \mathrm{~ms}\). d) Both (a) and (c) are true. e) Both (b) and (c) are true.
See all solutions

Recommended explanations on Physics Textbooks

Radiation

Read Explanation

Energy Physics

Read Explanation

Translational Dynamics

Read Explanation

Electricity and Magnetism

Read Explanation

Physical Quantities And Units

Read Explanation

Quantum Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free