Chapter 26, Problem 48P

To determine

The speed of rocket B relative to A.

Answer to Problem 48P

  $0.70c$

Explanation of Solution

Given info:

Speed of Rocket A is $0.75c$ .

Rocket B passes earth moving $0.95c$ relative to earth in the same direction.

Formula used:

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

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, $3.00\times {10}^{8}m/s$

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

Calculation:

The speed of rocket B relative to Earth can be written as

  $0.95c=\frac{\left(0.75c+u\text{'}\right)}{1+\frac{0.75u\text{'}}{c}}$

  $u\text{'}=0.70c$

Conclusion: The required value is $0.70c$ .