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 $0.280 \mathrm { c }$, and the second piece moves in the opposite direction with a speed $0.600 \mathrm { c }$. What is the rest mass of the second piece?
A) $73.9 \mathrm {~kg}$
B) $88.7 \mathrm {~kg}$
C) $79.6 \mathrm {~kg}$
D) $52.7 \mathrm {~kg}$
E) $68.8 \mathrm {~kg}$

Question

Quizplus · Accepted Answer

The correct answer is A because the total momentum of the system is zero, so the momentum of the two pieces must be equal and opposite. The momentum of the first piece is $190 \mathrm {~kg} \times 0.280 \mathrm { c } = 53.2 \mathrm {~kg} \cdot \mathrm { c }$, so the momentum of the second piece must be $-53.2 \mathrm {~kg} \cdot \mathrm { c }$. The rest mass of the second piece is then $53.2 \mathrm {~kg} / 0.600 \mathrm { c } = 73.9 \mathrm {~kg}$.

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