A ball projected from ground vertically upward is at same height at time `t_(1) and t_(2)`. The speed of projection of ball is [Neglect the effect of air resistance ]

Options

A. `(g(t_(1)+t_(2)))/(2)`q
B. `(g(t_(1)-t_(2)))/(2)`
C. `g(t_(1)+t_(2))`
D. `g(t_(1)-t_(2))`

Answer

a

Explanation

Let us assume the upwarde direction as the positive direction and h be the desired height mentioned in the question. We can use the following equation of motion.
`S=ut+(1)/(2)at^(2)`
`rArr h=ut-(1)/(2)gt^(2)`
`rArr gt^(2)-2at+2h=0`
`t_(1)` and `t_(2)` are the two roots of the above equation we can write sum of the roots as follows:
`t_(1)-t_(2)=(2u)/(g)`
`rArr u=(g(t_(1)-t_(2)))/(2)`