Calculating Momentum and Speed in a Father-Son Push Scenario

[astru025]

Homework Statement

A father (m = 86 kg) and son (m = 45 kg) are standing facing each other on a frozen pond. The son pushes on the father and finds himself moving backward at 3 m/s after they have separated. How fast will the father be moving?

Homework Equations

P=mv ( mass x velocity)
P=(m1 + m2) v

The Attempt at a Solution

(45+86) 3= 393. I have tried many different things and can't seem to come up with the answer.

 

[Abhilash H N]

Try to apply law of conservation of momentum...

 

[Chestermiller]

Momentum is a vector, so you need to use vectors (including their direction). Let i be a unit vector in the positive x direction, and let -i be a unit vector in the negative x direction. Suppose the boy is moving in the positive x direction after the push. What direction is the father moving after the push? What is the starting momentum of the father and son? If momentum is conserved, what is the final momentum of the father and son? What is the momentum of the son after the push? If v is the speed of the father after the push, what is his momentum after the push (in terms of v)?