# Determine the angle of the neutron

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 move off at an angle θ'2 = 45° from the neutron's initial direction. The neutron's initial speed is 7.0 × 105 m/s.

a) Determine the angle of the neutron, θ'1, measured from its initial direction.
_____°

b) What is the speed of the neutron, vn', after the collision?
_____m/s

c) What is the speed of the helium nucleus, vHe', after the collision?
_____m/s

x direction: m1*7.0x10^5+0=m1*v1'*Cosθn+4*m1*v2'*Cos45

y direction: 0=-m1*v1'*Sinθn+4*m1*v2'*Sin45

Change in KE: 1/2*m1*(7.0x10^5)^2=1/2*m1*v1'^2+1/2*4*m1*v2'^2

I know mass cancels and I need to do algebra to figure out the answer, but I am having trouble doing the algebra with so many unknowns.
Can anyone lend me a helping hand?

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