Question

A rocket fires a projectile at a speed of $0.95c$while traveling past the earth. Does an earthbound scientist measure the projectile’s speed to be $0.90c$What was the rocket’s speed as a fraction of $c$?

Short answer

As a fraction of $c$, the speed of a rocket is $0.345c$(since a negative sign indicates that the projectile and rockets are moving in the opposite direction.)

Step-by-step solution

Given Information 

We need to find the rocket’s speed as a fraction of $c$.

Simplify

Consider the velocity of the rocket is $v$. The projectile was thrown from the rocket, then the velocity will add up, and the velocity will be measured by the scientist from earth using the velocity addition formula

$$\begin{gathered} v_r=\frac{u+v}{1+{\displaystyle \frac{uv}{c^2}}} \\ \Rightarrow 0.9c=\frac{u+0.95c}{1+{\displaystyle \frac{0.95c\times v}{c^2}}} \\ \Rightarrow v=-0.345c \end{gathered}$$

Hence, the speed of the rocket will be $0.345c$(since a negative sign indicates that the projectile and rockets are moving in opposite direction.)