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## Homework Statement

A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to rebound at an angle Theta2 = 45° from the neutron's initial direction. The neutron's initial speed is 6.6x 10^5 m/s.

Determine the angle at which the neutron rebounds, O, measured from its initial direction.

What is the speed of the neutron after the collision?

What is the speed of the helium nucleus after the collision?

## Homework Equations

Conservation of KE

Conservation of momentum

1/2M1V1^2= 1/2M1V'1^2 + 1/2M2V'2^2

M1V1=M1V'1*cosO + M2V2cos45

0=M1V'1*sinO + M2V'2sin45

M2=4M1

V1=V'1 + 2*V'2

V1=V'1*cosO + 4*V'2*cos45

V'1*sinO= 4*V'2*sin 45

## The Attempt at a Solution

I have 3 equations and 3 unknows (V'1, V'2, O) I tried solving for O and it becomes a huge mess. Is there a simple way to do this? Or do I really have to figure out all this mess? Any help and tips are appreciated.

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