How much potential energy in the girl's body is converted into mechanical energy of the boy–girl system

The complete question is:

A 65 kg boy and his 40 kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 2.90 m/s toward the west. Ignore friction."

How much potential energy in the girl's body is converted into mechanical energy of the boy–girl system?

The ammount of potential energy converted to mechanical energy is 717 Joules

Explanation:

Knowing the Law of Momentum Conservation we can state that the momentum change of the boy is equal to and opposite of the momentum change of the girl.

Written in a formula:

where

Solving for :

Finally, using the energy conservation formula: