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)0 m/s
B)0.38 m/s
C)0.43 m/s
D)0.50 m/s
E)1.0 m/s

Question

Quizplus · Accepted Answer

In this scenario, the law of conservation of momentum applies, which states that the total momentum of an isolated system remains constant if no external forces act on it. Initially, the total momentum of the two spacemen is zero.

When spaceman A pushes B away from him with a certain force, there is an equal and opposite force acting on A (Newton's third law). As a result, the two spacemen will move in opposite directions such that the total momentum of the system remains zero.

Let's denote the final recoil speed of A by v. According to the law of conservation of momentum,

(mass of A) x (initial velocity of A) + (mass of B) x (initial velocity of B) = (mass of A) x (final velocity of A) + (mass of B) x (final velocity of B)

Plugging in the given values, we obtain:

(120 kg)(0 m/s) + (90 kg)(0 m/s) = (120 kg)(v) + (90 kg)(0.5 m/s)

Solving for v, we get:

v = 0.38 m/s

Therefore, the answer is B.

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