4) [ 20 pts ] In a game of Quidditch, there is a shot on goal with an empty net. Seeing this, a beater down the field hits a Bludger toward the Quaffle to change its path. The Quaffle (sphere A, mass ma) is initially moving in the y direction at a speed va. At the instant of the impact, the Bludger (sphere B, mass ma) is moving with a speed of va and hits sphere A along the line connecting the sphere centers, as shown. For those not familiar with Harry Potter terminology: A large red sphere (mass ma) is moving in the positive y direction at a velocity of Va. A blue sphere (mass ma) with a velocity of va collides with it from an oblique angle, deflecting it off its original path. Sphere A: mass ma = 0.4 kg; speed 12 m/s Sphere B: mass ma = 1.2 kg; speed 32 m/s Impact coefficient of restitution e = 0.8 Based on the information given and the diagram shown, determine the final velocity of sphere A (x and y components or magnitude and direction relative to the x axis) Note: the radius of sphere A is 2x the radius of sphere B, as shown, and at the instant of impact the center of sphere B is lined up with the edge of sphere A. Hint: First determine the orientation of the line of impact, shown as 0, in the graphic. If you are unable to determine this, you will lose points but can use an angle of 40° for the remainder of the problem.

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