Head-on Proton Collision: Finding Speed

[kevykevy]

Question - Two protons, separated by a large distance, are fired directly at each other. The closest approach in this head-on collision is 3.0 x 10^14 m. One proton starts with two times the speed of the other. Assuming there is no delection from the original path, determine the initial speed of each proton.

Solution - I read through my notes and textbook but I couldn't find any way to connect speed with this question. Is there any specific equations to use?

 

[nrqed]

Question - Two protons, separated by a large distance, are fired directly at each other. The closest approach in this head-on collision is 3.0 x 10^14 m. One proton starts with two times the speed of the other. Assuming there is no delection from the original path, determine the initial speed of each proton.

Solution - I read through my notes and textbook but I couldn't find any way to connect speed with this question. Is there any specific equations to use?

Conservation of energy.

the total energy is $${1 \over 2} m_1 v_1^2 + {1 \over 2} m_2 v_2^2 - {k q_1 q_2 \over r}$$ and it is conserved.

 

[kevykevy]

So, since I don't know what the mass is or the speed, would I split the question up into two parts, the first being at collision so I can solve for mass since speed is zero. Then I can use the law of conservation of energy to find velocity at start?

 

[kevykevy]

Actually, how would I solve that if there is 3 unknowns: mass, velocity, and charge?