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?
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
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.