A ball is thrown vertically upwards from the ground. It crosses a point at the height of 25 m twice at an interval of 4 secs. The ball was thrown with the velocity of

Options

A. `20 m//sec`
B. `25 m//sec`
C. `30 m//sec`
D. `35 m//sec`

Answer

C

Explanation

Let initial velocity of the ball `= u`
`:. 25 = ut - (1)/(2) g t^2 = ut - 5t^2`
`rArr 5t^2 - ut + 25 = 0`
If `t_1 and t_2` are the two solutions,
Then, `t_2 - t_1 = sqrt((t_2 + t_2)^2 - 4 t_1 t_2)`
`rArr 4^2 = (u^2)/(25) - 4 xx (25)/(5)`
`rArr 16^2 = (u^2)/(25) - 20 rArr u^2 = 25 xx 36`
`rArr u = 30 m//s`.