Two particles are projected obliquely from ground with same speed such that their range `'R'` are same but they attain different maximum heights `h_(1)` and `h_(2)` then relation between `R, h_(1)` and `h_(2)` is:

Options

A. `R = sqrt(h_(1)h_(2))`
B. `R = sqrt(2h_(1)h_(2))`
C. `R = 2 sqrt(h_(1)h_(2))`
D. `R = 4 sqrt(h_(1)h_(2))`

Answer

D

Explanation

`R = (u^(2)sin theta)/(g)` at angles `theta` and `90^(@) - theta`
Now, `h_(1) = (u^(2)sin^(2)theta)/(2g)` and `h_(2) = (u^(2)sin^(2)(90^(@)-theta))/(2g) = (u^(2)cos^(2)theta)/(2g)`
`h_(1)h_(2) = ((u^(2)sin 2theta)/(g)) (1)/(16) = (R^(2))/(16)`
`:. R = 4 sqrt(h_(1)h_(2))`