From the top of a tower, a stone is thrown up and it reaches the ground in time ` t_1 `A second stone is thrown down with the same speed and it reaches the ground in time `t_2` A third stone is released from rest and it reaches the ground in time The correct relation between ` t_1,t_2` and `t_3` is :

Options

A. `t_(3) = ((t_(1)+t_(2)))/2`
B. `t_(3)=sqrt(t_(1)t_(2))`
C. `1/t_3=1/t_1+1/t_2`
D. `t_(3)^(2) =t_(2)^(2) -t_(1)^(2)`

Answer

B

Explanation

When stone is thrown vertically upwards from the top of town of height h , then
`h = "ut"_(1) +1/2 "gt"_(1)^(2) " "...(i) `
When stone is thrown vertically downwards from the top of tower , then
`h = "ut"_(2) +1/2 "gt"_(2)^(2) " "...(ii) `
When stone is released from the top of tower , then
`h=1/2 "gt"_(3)^(2) " "....(iii)`
From equation (i) , we get `h/t_(1) = -u +1/2 "gt"_(1) " " ` (iv)
From equation (ii), we get `h/t_2 = u +1/2 "gt"_(2) " "...(v) `
`h(1/t_1+1/t_2)=1/2g(t_1+t_2)" or "h=1/2"gt"_1t_2`
Adding equation (iv) and (v) , we get
Putting the value in equation (iii) , we get `t_(3) =sqrt(t_1t_2)`