On an ice skating rink, a girl of mass 50 kg stands stationary, face to face with a boy of mass 80 kg. The children push off of one another, and the boy moves away with a velocity of + 3 m/s. What is the final velocity of the girl?

Assuming that the collision above is elastic, then the momentum and kinetic energy is conserved. To determine the final velocity, we make balances on momentum and kinetic energy and obtain the expression for the final velocity of the girl:

v'1 = (m1-m2) v1 / (m1+m2) + 2m2v2 / (m1+m2)

since v1 is zero, then

v'1 = 2m2v2 / (m1+m2)

v'1 = 2 (80) (3) / (50+80)

v'1 = 3.69 m/s