A ball of the mass 400gm is dropped from a height of 5m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100N so that it attains a vertical height of 20m. The time for which the ball remains in contect 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(2xx10xx5)` or `vec(v)_(1)=+10m//s=10m//s` .
Velocity of rebound
`v_(2)=sqrt(2gh_(1))=sqrt(2xx10xx20)=20m//s` or `vec(v)_(2)=-20m//s` .
`F=m(dv)/(dt)=(m(vec(v)_(2)-vec(v)_(1)))/(dt)=(0.4(-20-10))/(dt)=100N`.
by solveing, `dt=0.012` sec.