A `70 g` ball B dropped from a height `h_(0) = 9m` reaches a height `h_(2) = 0.25 m` after bouncing twice from identical `210 g` plates. Plate A rests directly on hard ground, while plate C rests on a foam-rubber mat. Determine
(i) the coefficient of restituation between the ball and the plates,
(ii) the height `h_(1)` of the ball's first bounce.

Answer

(i) `0.66` (ii) `4 m`

Explanation

For first collision with plate A, final velocity of ball `v_(1) = ev_(0) = e sqrt(2gh_(0))` ….(i)
For second collision `mv = 4mv' rArr v' = (v)/(4)`
`rArr e sqrt((2gh_(0))/(4)) = sqrt(2gh_(2)) rArr e = (2)/(3)`
Height attained after first collision
`:. h_(1) = e^(2)h_(0) = (2)/(3) xx (2)/(3) xx 9 = 4m`