Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 26: Problem 31

As observed from Earth, rocket Alpha moves with speed \(0.90 c\) and rocket Bravo travels with a speed of \(0.60 c\) They are moving along the same line toward a head-on collision. What is the speed of rocket Alpha as measured from rocket Bravo? (tutorial: adding velocities)

Short Answer

Expert verified
Answer: The relative velocity of rocket Alpha as seen from rocket Bravo is approximately 0.65217c or 65.217% of the speed of light.

Step by step solution

01

Identify the given information

We are given the velocities of rocket Alpha and rocket Bravo as observed from Earth or in the Earth's frame. - Velocity of rocket Alpha, \(v_A = 0.90c\) - Velocity of rocket Bravo, \(v_B = 0.60c\) We want to find the velocity of rocket Alpha as measured from rocket Bravo.
02

Apply the Einstein velocity addition formula

The Einstein velocity addition formula is used to add velocities in Special Relativity. The formula is given by: \(u = \frac{v_A + v_B}{1 + \frac{v_A v_B}{c^2}}\) where \(u\) is the relative velocity of rocket Alpha as measured from rocket Bravo, \(v_A\) is the velocity of rocket Alpha, \(v_B\) is the velocity of rocket Bravo, and \(c\) is the speed of light.
03

Insert the given values into the formula and solve

Plugging the given values into the formula, we get: \(u = \frac{0.90c - 0.60c}{1 + \frac{(0.90c)(-0.60c)}{c^2}}\) Notice that for rocket Bravo, its speed is in the opposite direction, so its value becomes negative. Simplify the expression and solve for \(u\): \(u = \frac{0.30c}{1 - 0.54}\) \(u = \frac{0.30c}{0.46}\) \(u = 0.65217c\)
04

Report the final answer

The speed of rocket Alpha as measured from rocket Bravo is approximately \(0.65217c\) or \(65.217\%\) 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

A starship takes 3.0 days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took 4.0 days. How fast did the starship travel, relative to that space station?
A plane trip lasts \(8.0 \mathrm{h} ;\) the average speed of the plane during the flight relative to Earth is \(220 \mathrm{m} / \mathrm{s}\). What is the time difference between an atomic clock on board the plane and one on the ground, assuming they were synchronized before the flight? (Ignore general relativistic complications due to gravity and the acceleration of the plane.)
An astronaut has spent a long time in the Space Shuttle traveling at $7.860 \mathrm{km} / \mathrm{s} .$ When he returns to Earth, he is 1.0 s younger than his twin brother. How long was he on the shuttle? [Hint: Use an approximation from Appendix A.5 and beware of calculator round off errors.]
Show that each of these statements implies that \(v<c\) which means that \(v\) can be considered a nonrelativistic speed: (a) $\gamma-1<<1 \text { [Eq. }(26-14)] ;\( (b) \)K<<m c^{2}\( [Eq. \)(26-15)] ;(\text { c }) p<m c[\text { Eq. }(26-16)] ;\( (d) \)K \approx p^{2} /(2 m)$.
Kurt is measuring the speed of light in an evacuated chamber aboard a spaceship traveling with a constant velocity of \(0.60 c\) with respect to Earth. The light is moving in the direction of motion of the spaceship. Siu- Ling is on Earth watching the experiment. With what speed does the light in the vacuum chamber travel, according to Siu-Ling's observations?
See all solutions

Recommended explanations on Physics Textbooks

Dynamics

Read Explanation

Linear Momentum

Read Explanation

Measurements

Read Explanation

Geometrical and Physical Optics

Read Explanation

Space Physics

Read Explanation

Fluids

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