Question

A 95 kg man lying on a surface of negligible friction shoves a 65 g stone away from himself, giving it a speed of 4.0 m/s. what speed does the man acquire as a result?

Answer 1

Total momentum of the system must stay constant, so M1*V1 = -M2*V2. Substituting in the values and rearranging, we find -V2 = M1*V1 / M2. 65 grams = 0.065 kg, so
0.065kg * 4.0m/s / 95kg = -2.7*10^-3 m/s. The negative indicates he is travelling in the opposite direction as the stone. Speed is independent of direction, so the final answer is 2.7*10^-3 m/s.

Answer 2

We can solve this problem by conserving linear momentum.
We have then that:
P1 = P2
m1v1 + m2v2 = m1v1 '+ m2v2'
Substituting values and clearing:
95 (0) + 0.065 (0) = 95v + 0.065 (4)
0 = 96v + 0.26
96v = -0.26
v = -0.0027 m / s
The man moves in the opposite direction to the stone.
answer:
the speed that a man acquire as a result is v = -0.0027 m / s