Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 36: Q. 26 (page 1060)

A rocket travels in the x-direction at speed 0.60c with respect to the earth. An experimenter on the rocket observes a collision between two comets and determines that the spacetime coordinates of the collision are (x',t')=(3.0×1010m,200s). What are the spacetime coordinates of the collision in earth’s reference frame?

Short Answer

Expert verified

γ=1.25x=8.25×1010mt=325s

Step by step solution

01

Given Information

We have given that a rocket travels in the x-direction at speed 0.60cwith respect to the earth.

The collision's spacetime coordinates are(x',t')=(3.0×1010m,200s).

We have to find the spacetime coordinates of the collision in earth’s reference frame.

02

Simplify

We have,

γ=1-vc2-1/2γ=1-(0.6)2-1/2γ=1.25

Lorentz transformation in Earth's frame yields:

x=γ(x'+vt')=1.23×1010m+(0.6)(3×108m/s)(200)=8.25×1010mt=γt'+vx'c2=1.25200+(0.6)(3×108m/s)(3×1010m)(3×108m/s)2=325s

Therefore,

γ=1.25x=8.25×1010mt=325s

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

The star Delta goes supernova. One year later and 2.0lyaway, as measured by astronomers in the galaxy, star Epsilon explodes. Let the explosion of Delta be at role="math" localid="1649750409129" xD=0 andtD=0. The explosions are observed by three spaceships cruising through the galaxy in the direction from Delta to Epsilon at velocitiesv1=0.30c, v2=0.50c, and v3=0.70c. All three spaceships, each at the origin of its reference frame, happen to pass Delta as it explodes.

a. What are the times of the two explosions as measured by scientists on each of the three spaceships?

b. Does one spaceship find that the explosions are simultaneous? If so, which one?

c. Does one spaceship find that Epsilon explodes before Delta? If so, which one?

d. Do your answers to parts b and c violate the idea of causality? Explain.

a. At what speed, as a fraction of c,must a rocket travel on a journey to and from a distant star so that the astronauts age 10years while the Mission Control workers on earth age 120years?

b. As measured by Mission Control, how far away is the distant star?

You fly 5000kmacross the United States on an airliner at 250m/s.You return two days later at the same speed.

a. Have you aged more or less than your friends at home?

b. By how much?

Hint: Use the binomial approximation

Two events in the reference frame Soccur 10msapart at the same point in space. The distance between the two events is2400msin the reference frame S'.

a. What is the time interval between the events in reference frame S'′?

b. What is the velocity of S'relative to S?

Derive the Lorentz transformations for tand t'.

Hint: See the comment following Equation 36.22.
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Translational Dynamics

Read Explanation

Famous Physicists

Read Explanation

Space Physics

Read Explanation

Force

Read Explanation

Astrophysics

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