A cue ball of mass m1 = 0.34 kg is shot at another billiard ball, with mass m2 = 0.575 kg, which is at rest. The cue ball has an initial speed of v = 7.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on.

a) write an expression for the horizontal component of the billiard ball's velocity, vr after the collision, in terms of the other variables of the problem.
b) what is this velocity, in meters per second?
c) Write an expression for the horizontal component of the cue ball's velocity, vr, after the collision.
d) what is the horizontal component of the cue ball's final velocity, in meters per second?

Part(a): The expression for the velocity of the billiard ball is

Part(b): The value of the velocity of the billiard ball is .

Part(c): The expression for the velocity of the cue ball is

Part(d): The value of the velocity of the cue ball is .

Explanation:

Given:

The mass of the cue ball, .

The mass of the billiard ball, .

The initial velocity of the cue ball,

The initial velocity of the billiard ball,

(a)

Consider the final velocity of the cue ball be and the final velocity of the billiard ball be .

From the conservation of linear momentum , we can write

From the conservation of energy, we can write

Dividing equation (1) by equation (2), we have

Rearranging equation (3) for , we have

Substitute equation (4) in equation (1), we can write

Substituting for , for and for in equation (5), we have

(b)

Substituting for , for and for in equation (6), we have

(c)

Rearranging equation(3) for , we have

Substitute equation (7) in equation (1), we can write

Substituting for , for and for in equation (8), we have

(d)

Substituting for , for and for in equation (9), we have

Negative sign indicates that the cue ball will bounce back.