Photon energy, momentum, and velocity

[warfreak131]

Homework Statement

Suppose one photon has an energy of 200 MeV and it is traveling along the x-axis. Suppose another has an energy of 100 MeV and is traveling along the y-axis. (A) What is the total energy of this system. (The answer is 300 MeV) (B)If a single particle has this same energy and momentum, what would be its mass?

The answer is 200 MeV, I am having trouble reaching that answer.

Homework Equations

$$p=\frac{E}{c}$$ for a photon
$$p={\gamma}mu$$ for a particle with mass
$$E=cp$$ for a photon
$$E={\gamma}mc^{2}$$ for a moving particle with mass.

The Attempt at a Solution

Energy of the photon = energy of the moving particle:
$$cp={\gamma}mc^{2}$$
$$300 MeV={\gamma}mc^{2}$$

Momentum of the photon = momentum of the moving particle:
$$\frac{E}{c}={\gamma}mu$$
$$\frac{300 MeV}{c}={\gamma}mu$$

This is all I can do so far, after this I get stuck. If I continue, I get the result that u=c. The correct answer is u=.74c

 

[betel]

The total momentum of the system of the two photons is not 300 MeV. Momentum is a vector so you have to add the vectors in the correct way.