A small bouncy ball of mass 37 g is held just above a football (the spherical, o

Question

A small bouncy ball of mass 37 g is held just above a football (the spherical, or truncated icosahedral, variety used in 'soccer') of mass 425 g. With their centers vertically aligned, both balls are released from rest at the same time and fall a distance of 1.5 m, before the football hits the ground. Assume that an elastic collision with the ground instantaneously reverses the velocity of the football while the bouncy ball is still moving down. Next the two balls collide elastically. Find the height to which the bouncy ball rises subsequent to this collision.

Explanation / Answer

velocity of football = sqrt(2gh) = sqrt(2 x 9.8 x 1.5) = 5.422 m/s = speed of bouncy ball

now as elastic collision after collision speed of bouncy ball,

v = [(37-425)(-5.422) + 2 x 425 x 5.422]/(37 + 425) = 14.53 m/s

so height attained = v2/2g = 10.77 m

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