A classical mechanics problem by Stuti Malik

A ball, initially at rest, is left free to accelerate vertically downward due to gravity from a hight of 9.8 meter. When the ball hits the ground, it rebounds and continues bouncing for some time. The coefficient of restitution between the ball and the ground is 0.5

The total time taken, in seconds, since the ball starts accelerating downwards and till it finishes bouncing is k√2, where k is an integer. Find k.

*Assume that the acceleration due to gravity is 9.8 m/s^2 and the air resistance is negligible.

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