What is the direction of the neutron's velocity after the collision?

[oy_katet]

Homework Statement

A neutron (mass 1.7x10^-27 kg) traveling at 2.7 km/s hits a stationary lithium nucleus (mass 1.2x10^-26 kg). Afterwards, the velocity of the lithium nucleus is 0.40 km/s at 54° to the original direction of the motion of the neutron. If the speed of the neutron after the collision is 2.5 km/s, in what direction is it traveling?

[Answer: 66° from initial direction of neutron's velocity]

Homework Equations

Givens:

m₁= 1.7x10^-27 kg
v_1x= 2.7 km/s

v'_1x= (2.5)cosθ
v'_1y= -(2.5)sinθ

m₂= 1.2x10^-26 kg
v_2x= 0 km/s

v'_2x= (0.4)cos54°
v'_2y= (0.4)sin54°

Equations:

m₁v_1x= m₁v'_1x+m₂v'_2x

0= m₁v'_1y+ m₂v'_2y

The Attempt at a Solution

I plugged in my values into the two equations, and for the first equation using the x-values I got θ= 65.42° and the second using the y-values I got 65.51°. I was wondering if anyone could point me in the right direction?

I've attached a diagram of my thought process.

 

[gneill]

The values given are probably not very precise, and very probably rounded; they are specified with only two significant digits. Accordingly, you can expect a little "slop" in the results. Believe only two digits, with the second being a bit "fuzzy"