Initial Velocity and Energy Conservation for Disk Collision

[xxphysics]

Homework Statement

Disk P (inertia 0.41 kg ) moves at an unknown velocity across a low-friction horizontal surface and collides with disk Q (inertia 0.75 kg ), which is initially at rest. After the collision, the two (now slightly dented) disks move apart without spinning. Velocity information is provided in the initial and final top-view diagrams in the (Figure 1) .

What was the initial velocity of disk P?
What fraction of the initial kinetic energy is converted during the collision?

Homework Equations

v1im1 + v2im2 = v1fm1 + v2fm2

The Attempt at a Solution

So I know you use conservation of momentum, but I'm not entirely sure how to set up the equations to include theta.

 

[TSny]

Momentum is a vector quantity. So, the relevant equation is a vector equation

m₁ v_1i + m₂ v_2i = m₁ v_1f + m₂ v_2f

In terms of x components:

m₁ v_1ix + m₂ v_2ix = m₁ v_1fx + m₂ v_2fx

(There is a similar equation for the y components.)