Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 26, Problem 45P

(a)

To determine

The speed of second spaceship relative to Earth when it moves in direction of first spaceship.

(a)

Expert Solution
Check Mark

Answer to Problem 45P

  0.98c

Explanation of Solution

Given info:

Speed of first spaceship with respect to the earth is v=+0.71c .

Speed of second spaceship is u'=+0.87c

Formula used:

  u=(v+u')1+vu'c2

Where,

  m is relativistic mass

  v is velocity (with the respect to the earth)

  u' is a second speed (or speed respect to first speed)

  c is speed of light, 3.00×108m/s

Note: If u' is in the opposite direction from v then u' must have a minus sign in the above mentioned expression.

Calculation:

Take positive direction in the direction of the first spaceship.

In the reference frame of the earth, first spaceship is moving at +0.71c and the second spaceship is moving at +0.87c relative to the first.

So, speed of the second spaceship relative to the first is

  u=(0.71c+0.87c)1+(0.71)(0.87)=0.98c

(b)

To determine

The speed of second spaceship relative to the Earth when it moves directly backward towards Earth.

(b)

Expert Solution
Check Mark

Answer to Problem 45P

The answer is 0.42c

Explanation of Solution

Given info:

Speed with respect to the earth is v=+0.71c .

Speed of second spacecraft is u'=0.87c .

Formula used:

  u=(v+u')1+vu'c2

Where,

  m is relativistic mass

  v is velocity (with the respect to the earth)

  u' is a second speed (or speed respect to first speed)

  c is speed of light, 3.00×108m/s

Note: If u' is in the opposite direction from v then u' must have a minus sign in the above mentioned expression.

Calculation:

Take positive direction in the direction of the first spaceship.

In the reference frame of the earth, first spaceship is moving at +0.71c and the second spaceship is moving at 0.87c relative to the first.

So, speed of the second spaceship relative to the Earth is

  u=(0.71c+(0.87c))1+(0.71)(0.87)=0.42c

Chapter 26 Solutions

Physics: Principles with Applications

Ch. 26 - Prob. 11QCh. 26 - Prob. 12QCh. 26 - Prob. 13QCh. 26 - Prob. 14QCh. 26 - Prob. 15QCh. 26 - Prob. 16QCh. 26 - Prob. 17QCh. 26 - Prob. 18QCh. 26 - Prob. 19QCh. 26 - Prob. 20QCh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Prob. 6PCh. 26 - Prob. 7PCh. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - Prob. 10PCh. 26 - Prob. 11PCh. 26 - Prob. 12PCh. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Prob. 15PCh. 26 - Prob. 16PCh. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - Prob. 21PCh. 26 - Prob. 22PCh. 26 - Prob. 23PCh. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Prob. 27PCh. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - Prob. 32PCh. 26 - Prob. 33PCh. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - Prob. 36PCh. 26 - Prob. 37PCh. 26 - Prob. 38PCh. 26 - Prob. 39PCh. 26 - Prob. 40PCh. 26 - Prob. 41PCh. 26 - Prob. 42PCh. 26 - Prob. 43PCh. 26 - Prob. 44PCh. 26 - Prob. 45PCh. 26 - Prob. 46PCh. 26 - Prob. 47PCh. 26 - Prob. 48PCh. 26 - Prob. 49GPCh. 26 - Prob. 50GPCh. 26 - Prob. 51GPCh. 26 - Prob. 52GPCh. 26 - Prob. 53GPCh. 26 - Prob. 54GPCh. 26 - Prob. 55GPCh. 26 - Prob. 56GPCh. 26 - Prob. 57GPCh. 26 - Prob. 58GPCh. 26 - Prob. 59GPCh. 26 - Prob. 60GPCh. 26 - Prob. 61GPCh. 26 - Prob. 62GPCh. 26 - Prob. 63GPCh. 26 - Prob. 64GPCh. 26 - Prob. 65GPCh. 26 - Prob. 66GPCh. 26 - Prob. 67GPCh. 26 - Prob. 68GPCh. 26 - Prob. 69GPCh. 26 - Prob. 70GPCh. 26 - Prob. 71GPCh. 26 - Prob. 72GPCh. 26 - Prob. 73GPCh. 26 - Prob. 74GP
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