Question

Imagine an unlikely situation where a cannon fires a cannon ball at $\left(0.7\right)c$ (seventy percent of the speed of light) relative to a train to which the cannon is attached. The train is moving at $\left(0.6\right)c$ (sixty percent of the speed of light) relative to the ground.
If an observer on the ground measured the speed of the cannon ball relative to the ground, what speed would he measure?

• A. Exactly $c$
• B. $\left(1.3\right)c$
• C. $\left(0.7\right)c$
• D. $\left(0.6\right)c$
• E. Between $\left(0.7\right)c$ and $c$

Answer 1

The correct option is E Between $\left(0.7\right)c$ and $c$

Speed of train w.r.t ground $v=0.6c$

Speed of cannon ball w.r.t train $v^{\prime }=0.7c$

According to relativity, speed of cannon ball w.r.t ground $v^{\prime \prime }=\frac{v+v^{\prime }}{1+v{v}^{\prime }}$

$\therefore$ $v^{\prime \prime }=\frac{0.6c+0.7c}{1+\left(0.6c\right)\left(0.7c\right)}=\frac{1.3c}{1.42}=0.915c$