Imagine you have a cue ball and three billiard balls, of equal mass, arranged as

Question

Imagine you have a cue ball and three billiard balls, of equal mass, arranged as shown in the diagram below.
a) (15pts) Determine the center of mass of this system.
b) (10pts) The cue ball is then shot at ball A with a speed of 3m/s. Assuming the balls to be point masses, calculate the center of mass of the system at the instant the balls collide.
c) (10pts) The two balls collide elastically, and ball A leaves the collision with a velocity entirely in the positive y direction. What is the final speed and direction of both the cue ball and ball A?

Explanation / Answer

1. Recall that the blocks can only move along the x axis. The x components of their velocities at a certain moment are v1x and v2x. Find the x component of the velocity of the center of mass (vcm)x at that moment. Express your answer in terms of m1, m2, v1x, and v2x [b]2. Keep in mind that, in general: v= dx/dt. [b]3. its the derivative of xcm = (m1x1 + m2x2) / (m1 + m2)...so does vcm= [(m1)(v1x) + (m2)(v2x)] / (m1 + m2) ?

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