(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a pool game, the cue ball, which has an initial speed of 8.0 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 30° to the original direction of the cue ball.

2. Relevant equations

V8 = Velocity of 8-ball

Vc = Velocity of cue ball

(1)Epx = m*V8*cos(30) + m*Vc*cos(x) = m*8

(2)Epy = m*V8*sin(30) + m*Vc*sin(x) = 0

(3).5*m*Vi^2 = .5*m*V8^2 + .5*m*Vc^2

3. The attempt at a solution

While these equations are technically solvable, they are nearly impossible by hand. Solving (3) for one velocity and using substitution twice I get:

sin(x)^2 -cos(30)*cos(x) + sin(30)*cos(30)*cos(x) - sin(30)*cos(x)^2 = -1/8

Is there an easier way to solve this since I know I will not be able to solve this equation myself?

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# Momentum and Elastic Collisions

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