A ball of mass 400 gm is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 newton so that it attains a vertical velocity of 20 m/s. The time for which the ball remains in contact with the bat is `(g=10m//s^(2))`

Options

A. `0.12s`
B. `0.08s`
C. `0.04s`
D. 12s

Answer

A

Explanation

Velocity by which the ball hits the bat
`v_(1) = sqrt(2gh_(1)) = sqrt(2 xx 10 xx 5) rArr v_(1) = - 10 m//s(hat(j))`
Velocity of rebound
`v_(2) sqrt(2 gh_(2)) = sqrt(2 xx 10 xx 20) rArr v_(2) = 20 m//s(hat(j))`
Force `F = (mdv)/(dt)`
`rArr F = (m Delta v)/(Delta t) = (m(v_(2) - v_(1)))/(Delta t)`
`rArr Delta t = (0.4(20-(-10)))/(100) rArr Delta t = 0.12 sec`