Aproton is traveling to the right at 2.0 * 107 m/s. it has a head on perfectly elastic collision with a carbon atom. the mass of the carbon atom is 12 times the mass of the proton.
what are the speed and direction of each after the collision?

(a) , in the initial direction of the proton.

(b) , in the opposite direction.

Solution:

As per the question:

Velocity of the proton,

If,

Mass of proton  be

Then

Mass of carbon atom,

Now, if the initial velocity of the proton be

Let the carbon atom be initially at rest with initial velocity

As the collision is perfectly elastic:

Using the principle of conservation of linear momentum:

            (1)

Using the conservation of energy:

Using eqn (1):

Solving the above quadratic eqn, we get:

Since, the velocity here is positive, i.e., the direction of the carbon atom is along the initial direction of proton.

Now, for the speed of the proton:

Negative sign here indicates that the movement of the proton is in the opposite direction.