In a pool game, the cue ball, which has an ini- tial speed of 2 m / s, makes an

Question

In a pool game, the cue ball, which has an ini- tial speed of 2 m/s, makes an elastic collision with the eight ball, which is initially at rest. The two balls have equal masses of 3 kg. Af- ter the collision, the eight ball moves at an an angle of 40 ? to the original direction of the cue ball.

What angle does the cue ball make with respect to the original line of motion?

Answer in units of ?.

Part B:

Find the speed of the cue ball. Answer in units of m/s.

Part C:

Find the speed of the eight ball. Answer in units of m/s.

Explanation / Answer

here,

initial speed of cue ball , u1 = 2 m/s

let the final speeds be v1 and v2

using conservation of momentum

m*u1 = m * v1*cos(theta) + m * v2 * cos(40)

2 = v1 * cos(theta1) + v2 * cos(40) ...(1)

and

m*v1 * sin(theta1) = m*v2 * sin(40)

v1 * sin(theta1) = v2 * sin(40) ....(2)

and

using conservation of kinetic energy

0.5 * m *u1^2 = 0.5 * m * v1^2 + 0.5 * m * v2^2

2^2 = v1^2 + v2^2 ....(3)

from (1) , (2) and (3)

v1 = 1.49 m/s

v2 = 1.33 m/s

theta = 35.01 degree

the anghle made by cue ball with original line of motion is 35.01 degree

B)

the speed of the cue ball is 1.49 m/s

C)

the speed of the eight ball is 1.33 m/s

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