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

Answer

C

Explanation

Let `u` be velocity of ball with which it is thrown.
`rArru(6)+(1)/(2)a(6)^(2)=420`
`rArr u+3a=70` ....`(ii)`
`h=ut+(-(1)/(2)g t^(2))25=ut-5t^(2)`
`5t^(2)-ut+25=0` Let `t_(1),t_(2)` be its roots
`t_(1)+t_(2)=u//5,t_(1)t_(2)=5`
Given, `t_(2)-t_(1)=4sec`.
`(t_(2)-t_(1))^(2)=16`
`rArr(t_(2)+t_(1))^(2)-4t_(1)t_(2)=16`
`((u)/(5))^(2)-4xx5=16u=30m//sec.`