Special relativity (A.P. French 7.5)

[ladybeetle]

Homework Statement

A particle of rest mass m and velocity v collides elastically with a stationary particle of rest mass M. Express the recoil and scattering angels in terms of the corresponding angles in the zero-momentum system. Show that your answers reduce to the non-relativistic ones if v<<c

Homework Equations

I think I have to show that (mc^2)/(1-(v/c)^2)^1/2 reduces to .5mv^2 by using the binomial theorem when v<<c. since momentum is related to kinetic energy.

The Attempt at a Solution

(not clear how to do it though) Please help me!

 

[vela]

That's not what the question is asking you to do. In the center-of-mass system, say the particle with mass m scatters at an angle of $\theta'$. What happens to the other particle? Now what does this collision look like as seen in the lab frame? What angle $\theta$ in the lab frame corresponds to the angle $\theta'$ in the COM frame?

Once you figure that out, you're supposed to show it reduces to the non-relativistic equivalents when v<<c.