Question

In a pool game, the cue ball, which has an initial speed of 7.0 m/s, make an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 25° to the original direction of the cue ball.

(a) Find the direction of motion of the cue ball after the collision (______) I got the 60° which is right.

(b) Find the speed of each ball. Assume that the balls have equal mass.

(_____m/s)

(_____m/s)

I posted this qustion so far two times and no one still got the right answer for part (b)

Answer 1

Let the cue ball be moving in x direction at 7 m/s

Mass of cue ball and 8 ball be m

Let the velocity of 8 ball be v 25 degree anticlockwise of + x axis

So velocity of 8 ball after collision = v cos 25 i + v sin 25 j

Let the velocity of cue ball be v_c theta degree clockwise of + x aixs after collision

So velocity of cue ball after collision =

Now momentum conservation in x direction:

=> (eq 1)

Momentum conservation in y direction

=> (eq 2)

Conservation of energy

=>    (eq 3)

Squaring and adding eq 1 and eq 2

(eq 4)

So comparing eq 4 and eq 3

=>

Replacing this value of theta in eq 1 and eq 2 and solving simultaneously gives

v_c = 2.9583 m/s

v = 6.3442 m/s

Answers. The direction of motion of the cue ball after the collision = 65 degree ( not 60 degree as you have said)

Velocity of cue ball = 2.9583 m/s

velocity of 8 ball = 6.3342 m/s