What Was the Initial Speed of the Proton in a Collision?

[kristjan]

Homework Statement

The moving proton hits the second proton, which we consider to be stationary. In the moment of central strike gap between the protons is 10(-13)m. What was the initial speed of the moving proton? Proton mass is 1.67*10(-27)kg and charge 1.6*10(-19) C.

Homework Equations

Electric potential energy U=kQq/r
Kinetic energy 1/2 mv2

The Attempt at a Solution

kinetic energy is transformed into electric potential energy at the point of closest approach:
electric potential energy=kinetic energy of moving proton
From there I find initial speed of moving proton to be v=1.66*10(6) m/s, in book answer is 2.35*10(6) m/s

 

[ehild]

Homework Statement

The moving proton hits the second proton, which we consider to be stationary. In the moment of central strike gap between the protons is 10(-13)m. What was the initial speed of the moving proton? Proton mass is 1.67*10(-27)kg and charge 1.6*10(-19) C.

Homework Equations

Electric potential energy U=kQq/r
Kinetic energy 1/2 mv2

The Attempt at a Solution

kinetic energy is transformed into electric potential energy at the point of closest approach:
electric potential energy=kinetic energy of moving proton
From there I find initial speed of moving proton to be v=1.66*10(6) m/s, in book answer is 2.35*10(6) m/s

Perhaps, the other proton was stationary at the beginning, but free to move. Then momentum is conserved.

 

[Chandra Prayaga]

Remark by ehild above is right. If it is asumed that the target proton is (somehow) held stationary, then I am also getting the same answer that kristjan got. If you assume that the target proton is free to move, and that it is a 1-dimensional collision problem, using (non-relativistic) momentum and energy conservation, I get the book answer.