Question

Two electrons one moving in opposite direction with speeds $0.8\,c$ and $0.4\,c$ where c is the speed of light in vacuum. Then the relative speed is about

• A. $0.4 \,c$
• B. $0.8 \,c$
• C. $0.9 \,c$
• D. $1.2 \,c$

Answer 1

Answer: (C)

$0.9 \,c$

Answer 2

The particles are moving with velocities $0.8 \,c$ and $-0.4\, c$ in the laboratory frame, say $S^{\prime}$ frame. Let $S$ be a reference frame in which the particle with velocity $-0.4\, c$ is at rest. Then, the velocity of $S^{\prime}$ (laboratory) relative to $S$ is $v=0.4\, c$. Therefore, the particle which in $S^{\prime}$ has velocity $u^{\prime}=+0.8\, c$ has a velocity in S given by
$u =\frac{u^{\prime}+v}{1+\frac{u^{\prime} v}{c^{2}}}$
$=\frac{0.8 c+0.4 c}{1+\frac{(0.8 c)(0.4 c)}{c^{2}}}$
$=\frac{1.2 c}{1+0.32}=0.9 c$