Frictionless shove - kinetic energy and momentum

[PacFan01]

Homework Statement

Edward and Jacob, standing face-to-face on a horizontal sheet of frictionless ice, push off each other, causing each to slide backward. Jacob is more massive than Edward. After the push, which of the two is moving faster?

Homework Equations

Conservation of momentum: P_i = P_f
Kinetic energy: K = 1/2mv²

The Attempt at a Solution

Intuitively, the answer to this problem is obvious (Edward is moving faster after the push). I also know that Edward's smaller mass means his acceleration must be greater so that F₁₂ = -F₂₁. However, this problem was assigned before our Force unit, so I would like an explanation of this phenomena in terms of momentum.

I don't know if this can be explained with conservation of momentum, because V_i = 0, so it is difficult compare their velocities in terms of momentum in a meaningful way. Also, we know that the momentum of the system is conserved, but that does not show, algebraically, that Edward is moving faster than Jacob after the push.

I am wondering if this problem can be solved using a kinetic energy equation, K = 1/2mv². This expression can show that, if the kinetic energies are equal, Speed_Ef > Speed_Ji. However, I do not know how to show that K_E = K_J.

Any help with an algebraic proof that Edward will be moving faster than Jacob after the push would be much appreciated.

 

[Simon Bridge]

You are over-thinking things. This is a conservation of momentum problem.