In a game of pool, the cue ball strikes the black 8 ball and sends it into the c

Question

In a game of pool, the cue ball strikes the black 8 ball and sends it into the corner

pocket. The cue ball initially travels at v = 1 m/s in the x direction. After the collision, the 8

ball makes an angle of ? = 45? with the x axis and is traveling at a speed v2. The cue ball is now

moving at an unknown angle ?1 with respect to the x axis at a speed v1. You may assume that the balls have the same mass and that the collision is elastic.

(a) Write the expression for energy conservation.

(b) Write equations for momentum conservation.

(c) Find the final speed of the 8 ball

Explanation / Answer

Conservation of Energy

energy of cue ball initially =energy of cue ball finally +energy of black ball

1/2 *m*1^2=1/2mv1^2+8*1/2*m*v^2

Momentum in x

M*1=M*8*V*COS45+M*V1*COSTHETA 1

CONSERVATION IN Y

8MVSIN45+MV1SINTHETA 1=0

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