A.) What was the speed vAi of puck A before the collision? B.) Calculate ΔK, the change in the total kinetic energy of the system?

On a frictionless horizontal air table, puck A (with mass 0.253 kg ) is moving toward puck B (with mass 0.366 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.649 m/s to the right.

For A, initial x momentum = 0.03 * 7.79 = 0.2337

Final x momentum = 0.03 * vA * cos 65

Final y momentum = 0.03 * vA * sin 65

For B, final x momentum = 0.06 * vB * cos 37

Final y momentum = -0.06 * vB * sin 37

0.03 * vA * cos 65 + 0.06 * vB * cos 37 = 0.2337

0.03 * vA * sin 65 + -0.06 * vB * sin 37 = 0

0.03 * vA * sin 65 = 0.06 * vB * sin 37

vA = 2 * vB * sin 65 ÷ sin 37

0.03 * (2 * vB * sin 65 ÷ sin 37) * cos 65 + 0.06 * vB * cos 37 = 0.2337

vB * (0.6 * sin 65 ÷ sin 37 cos 65 + 0.06 * cos 37) = 0.2337

vB = 0.2337÷ [(0.6 * sin 65 ÷ sin 37 * cos 65 + 0.06 * cos 37)]

vB = 0.2337 ÷ 0.42948519

This is approximately 0.544 m/s.

vA = 2 * (0.2337 ÷ 0.42948519) * sin 65 ÷ sin 37

This is approximately 1.63 m/s.

Check:

0.03 * 1.63* cos 65 + 0.06 * 0.544 * cos 37 ≈ 0.2327

Since I rounded the velocities, I believe that this proves that they are correct.

What was the speed vai of puck a before the collision?