Two balls colliding - relativity included

[aid]

Homework Statement

So, I am to describe the collision of two balls with equal masses in a relativistic manner. The energy of the first ball is given. They're asking me to compute the angle $$\phi$$ between the directions of the balls movement after the collision.

The Attempt at a Solution

From the conservation of energy I get:

$$\sqrt{m^2c^2 + p^2c^2} = \sqrt{m^2c^2 + p^{2}_1 c^2} + \sqrt{m^2c^2 + p^{2}_2 c^2}$$ (1)

From the conservation of momentum I get:

$$p^2 = p^{2}_1 + p^{2}_2 + 2 \vec p_1 \vec p_2$$ (2)

Since $$\vec p_1 \vec p_2$$ is equall to $$... \cos \phi$$, I hoped it would lead me to an straightforward answer. Unfortunately, I have no idea what to do next.

For example, taking square of (1):

$$m^2c^2 + p^2c^2 = m^2c^2 + p^{2}_1 c^2 + m^2c^2 + p^{2}_2 c^2 + 2 \sqrt{m^2c^2 + p^{2}_1 c^2} \sqrt{m^2c^2 + p^{2}_2 c^2}$$

and combining it with (2) I get:

$$\vec p_1 \vec p_2 = \frac{m^2}{2} + \sqrt{m^2 + p^{2}_1} \sqrt{m^2 + p^{2}_2}$$

But the above hardly helps me to achieve my goal. :/

 

[jbsteele]

In case it is of any use, I have the following information:m = 5 * 10^-26 kg p_1 = 2 * 10^-22 kg m/s I would be very thankful for any help.