A 0.015 kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a 0.015 kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 18.0 cm/s. A. Find the velocity of the second marble after the collision.
B. Verify your answer by calculating the total kinetic energy before and after the collision.

Given:

First marble:

Second marble,

(A)

As we know, the coefficient of restitution will be:

→

By putting the values,

By applying cross-multiplication,

            (velocity)

(B)

The initial K.E:

=

=

The final K.E:

=

=

Thus the responses above is right.

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Explanation:

mass of first marble

Initial velocity of the first marble

considering right side as positive

Mass of second marble

After collision first marble moves to the left with a velocity of 18 cm/s

i.e.

considering be the velocity of second marble after collision

The Coefficient of restitution is 1 for an elastic collision

Putting values

So, the velocity of the second marble is 22.5 m/s to the right after the collision

(b)Initial kinetic energy =

Final kinetic energy=