Speed of Particles Homework: E=mc^2, E=Bev, Answer (a)?

[soopo]

Homework Statement

The problem is at
http://dl.getdropbox.com/u/175564/physicsSpeedParticles.JPG

Homework Equations

The following equations may be useful
E = .5 mc^2
E = Bev

The Attempt at a Solution

The right answer is (a).
However, I am unsure how it is obtained.

For example, by comparing the energies of the two particles, we get only
(v1 / v2)^2 = (E1 / E2) * 2/167

where the energies are unknown.

 

[rl.bhat]

Consider the conservation of linear momentum.

 

[soopo]

Consider the conservation of linear momentum.

I get the following equation
v1 / v2 = (p1 / p2) * (234 / 4)

I assume that the momentum of the alpha particle equals that of the original particle.

This gives us the right answer

v1 / v2 = (234 / 4)
= 58.5

Thank you for your answer!