A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of $190 \mathrm {~kg}$ and moves away with a speed $0.500 c$, and the second piece has a rest mass of $250 \mathrm {~kg}$ and moves in the opposite direction. What is the speed of the second piece?
A) $0.212 c$
B) $0.473 c$
C) $0.500 c$
D) $0.402 c$
E) $0.380 c$

Question

Quizplus · Accepted Answer

The conservation of momentum principle applies, even in relativistic contexts. Since the satellite was initially at rest, the total momentum before the separation is zero. After separation, the momentum of the two pieces must still sum to zero to conserve momentum. The relativistic momentum of an object is given by $p = \frac{mv}{\sqrt{1 - v^2/c^2}}$, where $m$ is the rest mass, $v$ is the velocity of the object, and $c$ is the speed of light. Setting the momentum of the two pieces equal and opposite and solving for the unknown velocity yields the speed of the second piece as $0.402c$.

A Satellite, Initially at Rest in Deep Space, Separates into Two