Chapter 15, Problem 19A

If the spaceship in question 18 somehow travels at c relative to you, and it somehow fires its rocket at c relative to itself, use the equation to show that the speed of the rocket relative to you is still c!

To determine

To show: The speed relative speed of rocket relative to a person is c .

Explanation of Solution

Given:

Speed of spaceship relative to person, $v_1=c$

Speed of rocket relative to spaceship, $v_2=c$

Formula used:

The formula for addition of relative velocities is,

  $v=\frac{v_1+v_2}{1+\frac{v_1{v}_2}{c^2}}$

Calculation:

On substituting the given values in the given formula,

  $\begin{array}{l}v=\frac{c+c}{1+\frac{c\times c}{c^2}}\\ \Rightarrow v=\frac{2c}{2}=c\end{array}$

Conclusion:

Therefore, it is proved that the speed of rocket relative to person is c .