Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 140 kg and that of spaceman B is 100 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 m/s

The final recoil speed of A is -0.36 m/s

Explanation:

Given;

mass of spaceman A, m₁ = 140 kg

mass of spaceman B, m₂ = 100 kg

initial speed of spaceman A, u₁ = 0

initial speed of spaceman B, u₂ = 0

final speed of spaceman B, v₂ = 0.5 m/s

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

140 x 0 + 100 x 0 = 140v₁ + 100 x 0.5

0 = 140v₁ + 50

-50 = 140v₁

v₁ = -50/140

v₁ = -0.36 m/s

Thus, the final recoil speed of A is -0.36 m/s

The negative sign indicates that it moved in opposite direction of spaceman B