Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5 m/s. The final recoil speed of A is:
A) zero
B) 0.38 m/s
C) 0.5 m/s
D) 0.67 m/s
E) 1.0 m/s

Question

Quizplus · Accepted Answer

Momentum is conserved, so the total momentum before the push is zero, and the total momentum after the push is also zero. Therefore, the momentum of spaceman A after the push must be equal in magnitude but opposite in direction to the momentum of spaceman B. The momentum of spaceman B is 90 kg * 0.5 m/s = 45 kg*m/s. Therefore, the momentum of spaceman A must be -45 kg*m/s. The mass of spaceman A is 120 kg, so his recoil speed must be -45 kg*m/s / 120 kg = -0.375 m/s. However, since the question asks for the final recoil speed, we must take the absolute value of this value, which is 0.38 m/s.

Two Spacemen Are Floating Together with Zero Speed in a Gravity-Free