A body is projected verticallt upwards. If `t_(1)` and `t_(2)` be the times at which it is at a height h above the point of projection while ascending and descending respectively, then:

Options

A. `.^(1//2)g t_(1)t_(2)`
B. `g t_(1)t_(2)`
C. `2g t_(1)t_(2)`
D. `4 g t_(1)t_(2)`

Answer

A

Explanation

`O` to `A: h=ut_(1)-1/2g t_(1)^(2) …(i)`
`O` to `B`: `h=ut_(2)-1/2g t_(2)^(2) …(ii)`
Solving `u=g/2(t_(1)+t_(2))`
`h=1/2g t_(1) t_(2)`
OR
`h=ut-1/2g t^(2)`
`g t^(2)-2ut+2h=0`
Sum of roots, `t_(1)+t_(2)=-((-2u)/g)`
`implies u=g/2(t_(1)+t_(2))`
Product of roots, `t_(1) t_(2)=(2h)/2`
`impliesh=1/2g t_(1) t_(2)`