How do you solve part d? Two identical objects A and B of mass M move on a one-d

Question

How do you solve part d?

Two identical objects A and B of mass M move on a one-dimensional,horizontal air track. Object B initially moves to the rightwith speed v0. Object A initially moves to theright with speed 3v0, so that it collides with objectB. Friction is negligible. Express your answers to thefollowing in terms of M and v0.
a. Determine the totalmomentum of the system of the two objects.
b. A student predicts that the collisionwill be totally inelastic. Assuming this si true, determinethe following for the two objects immediately after thecollision.
i. the speed
ii. the direction of motion(left or right)

When the experiment is performed, the student is surprised toobserve that the objects separate after the collision and thatobject B subsequently moves to the right with a speed2.5v0.
c. Determine the following for object A immediately after thecollision.
i. the speed
ii. the direction of motion(left or right)
d. Determine the kinetic energy dissipated in the actualexperiment.

Explanation / Answer

KE = 1/2mv^2

so find 1/2m(v1)^2+1/2m(v2)^2 (the initial KE) and subtract off from them their final KE (1/2m(v3)^2+1/2m(v4)^2 )

so like for B it's final speed was 2.5v0, which means A must be 1.5v0.

So 1/2*m*(3)^2*v0+1/2*m*1^2*v0=1/2m(2.5)^2*v0+1/2*m*(1.5)^2*v0+loss
cancel out 1/2 m and v0

10-2.5^2-1.5^2=1.5 = loss

1.5/2*m*v0 = loss

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