Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 26: Problem 68

Suppose that as you travel away from Earth in a spaceship, you observe another ship pass you heading in the same direction and measure its speed to be $0.50 c .$ As you look back at Earth, you measure Earth's speed relative to you to be \(0.90 c .\) What is the speed of the ship that passed you according to Earth observers?

Short Answer

Expert verified
Answer: The speed of the ship that passed you according to Earth observers is approximately \(0.966c\).

Step by step solution

01

List the known values

We know the following speeds: - Speed of the spaceship relative to Earth: \(u = 0.90c\) - Speed of the other ship relative to you: \(v = 0.50c\) - Speed of light: \(c = 1\) (in natural units)
02

Substitute the values into the relativistic velocity addition formula

Now, we can substitute the values into the formula: $$ w = \frac{0.90c + 0.50c}{1 + \frac{(0.90c)(0.50c)}{c^2}} $$
03

Simplify the equation

To simplify the equation, we can cancel out \(c\) since it's equal to \(1\) in natural units: $$ w = \frac{0.90 + 0.50}{1 + (0.90)(0.50)} $$
04

Calculate the result

Now, we can perform the calculations: $$ w = \frac{1.40}{1 + 0.45} = \frac{1.40}{1.45} $$
05

Convert the result to the speed of light

To convert the result back to the speed of light, we can multiply by \(c\) (in this case, \(c=1\), so no need to multiply): $$ w = \frac{1.40}{1.45}c $$
06

Final answer

The speed of the ship that passed you according to Earth observers is: $$ w \approx 0.966c $$

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

Octavio, traveling at a speed of \(0.60 c,\) passes Tracy and her barn. Tracy, who is at rest with respect to her barn, says that the barn is 16 m long in the direction in which Octavio is traveling, \(4.5 \mathrm{m}\) high, and $12 \mathrm{m}$ deep. (a) What does Tracy say is the volume of her barn? (b) What volume does Octavio measure?
Consider the following decay process: \(\pi^{+} \rightarrow \mu^{+}+v .\) The mass of the pion \(\left(\pi^{+}\right)\) is \(139.6 \mathrm{MeV} / c^{2},\) the mass of the muon \(\left(\mu^{+}\right)\) is \(105.7 \mathrm{MeV} / c^{2},\) and the mass of the neutrino \((v)\) is negligible. If the pion is initially at rest, what is the total kinetic energy of the decay products?
An engineer in a train moving toward the station with a velocity \(v=0.60 c\) lights a signal flare as he reaches a marker \(1.0 \mathrm{km}\) from the station (according to a scale laid out on the ground). By how much time, on the stationmaster's clock, does the arrival of the optical signal precede the arrival of the train?
Two atomic clocks are synchronized. One is put aboard a spaceship that leaves Earth at \(t=0\) at a speed of \(0.750 c .\) (a) When the spaceship has been traveling for \(48.0 \mathrm{h}\) (according to the atomic clock on board), it sends a radio signal back to Earth. When would the signal be received on Earth, according to the atomic clock on Earth? (b) When the Earth clock says that the spaceship has been gone for \(48.0 \mathrm{h},\) it sends a radio signal to the spaceship. At what time (according to the spaceship's clock) does the spaceship receive the signal?
An extremely relativistic particle is one whose kinetic energy is much larger than its rest energy. Show that for an extremely relativistic particle $E \approx p c$.
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Particle Model of Matter

Read Explanation

Nuclear Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Radiation

Read Explanation

Waves 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