# Question #dffe3

##### 1 Answer

It is given that collision between the protons is elastic. We know that for such collisions both momentum and kinetic energy are conserved.

The total system kinetic energy before the collision equals to the total system kinetic energy after the collision.

Also, in a perfectly elastic collision coefficient of restitution is

Let two protons be designated as

Momentum of system before collision

Momentum of system after collision

By Law of conservation of momentum we have

Since it is proton-proton collision, mass of both is same. As such the above expression reduces in terms of velocities

From Law of Conservation of Energy we get

As mass of both protons is identical kinetic energy is shared equally between the two after the collision.

Inserting in(2) we get

Inserting given value