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.

which statement about this sum is true? −245+2.7

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.