Chapter 26, Problem 47P

To determine

The speed of the second pod relative to the first pod.

Answer to Problem 47P

  $0.92c$

Explanation of Solution

Given:

Speed of first spaceship is $-0.60c$

Speed of second spaceship is $+0.70c$

Formula used:

It is known that

  $u=\frac{\left(v+u\text{'}\right)}{1+\frac{vu\text{'}}{c^2}}$

Where,

  $m$ is relativistic mass

  $v$ is velocity (with the respect to the earth)

  $u\text{'}$ is a speed (Or speed respect to the first speed)

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

If $u\text{'}$ is in the opposite direction from $v$ then $u\text{'}$ must have a minus sign in the above mentioned expression.

Calculation:

From the first pod’s point of view, the spaceship and the second pod are moving in the same direction.

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

  $u=\frac{\left(0.60c+0.70c\right)}{1+\left(0.60\right)\left(0.70\right)}=0.92c$

Conclusion: The required value is $0.92c$ .