A95 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?

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.
 
 the speed that a man acquire as a result is v = -0.0027 m / s