A small metal spehre is released from a height of 2m. After striking the ground, it rises to a height of 1.28 m. What is the coefficient of restitution?

Options

A. `0.8`
B. `0.6`
C. `0.5`
D. `0.4`

Answer

A

Explanation

The distance covered by the ball during its fall is given by
`s = (1)/( 2) g t_(1)^(2) = (1)/( 2) xx g xx 4 = 2g ` `:. s_(1) = 2g `
After bouncing it rises to the highest point in 1s.
Considering the free fall from the highest point we get,
`s_(2) =( 1)/(2) g t_(2)^(2) = (1)/( 2) xx g xx1 = (g)/(2)`
But `e = sqrt((s_(2))/( s_(1)))= sqrt( (g)/( 2 xx 2g)) =sqrt((1)/(4)) =(1)/(2)`
`:. e = 0.5 `