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## Homework Statement

A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical

stationary ball as shown. If the first ball moves away with angle 30 ° to the

original path, determine

a. the speed of the first ball after the collision.

b. the speed and direction of the second ball after the collision.

## Homework Equations

m1v1 + m2v2 = m1v1' + m2v2'

1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2

## The Attempt at a Solution

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m1 = m2 = 2.0kg

v1 = 3.0m/s

v2 = 0m/s

theta1 = 30

In the x direction

m1v1 + m2v2 = m1v1'cos30 + m2v2'cos(theta2)

(2.0)(3.0) + (2.0)(0) = (2.0)v1'cos30 + (2.0)v2'cos(theta2)

masses cancel out to leave;

3.0 = v1'cos30 + v2'cos(theta2)

In the y direction

m1(0) + m2(0) = m1v1'sin30 + m2v2'sin(theta2)

masses cancel to leave:

-v1'sin30 = v2'sin(theta2)

Now here is where I am getting stuck. I know that I have to somehow combine the x and y equations as well as the conservation of NRG eqn to find the three unknowns, but I am lost as to how the algebra will work out. I think I have to square them somehow to eventually get cos^2(theta2) + sin^2(theta2) = 1 to get around the unknown theta... but everytime I have tried, it doesn't work out. Please help!

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