A ball is thrown upwards with a speed u from a height h above the ground.The time taken by the ball to hit the ground is

Options

A. `(upsilon)/(g) sqrt(1-(2hg)/(upsilon^(2)))`
B. `(upsilon)/(g)sqrt(1+(2hg)/(upsilon^(2)))`
C. `sqrt(1+(2hg)/(upsilon^(2)))`
D. `(upsilon)/(g)[1+sqrt(1+(2hg)/(upsilon^(2)))]`

Answer

D

Explanation

`-h=upsilon t-(1)/(2)g t^(2)` or `g t^(2)-2upsilon t-2h=0`
`therefore t=(2upsilon+sqrt(4upsilon^(2)+8gh))/(2g)=(upsilon)/(g)[1+sqrt(1+(2hg)/(upsilon^(2)))]`