Two particles are projected from the same point with the same speed `u` such that they have the same range `R`, but different maximum heights, `h_(1)` and `h_(2)`. Which of the following is correct ?

Explanation

For equal ranges, body should be projected with angle `theta` or `(90^@ - theta)` from the horizontal.
And for these angles :
`h_1 = (u^2 sin^2 theta)/(2 g) and h_2 = (u^2 cos^2 theta)/(2 g)`
By multiplication of both height,
`h_1 h_2 = (u^2 sin^2 theta cos^2 theta)/(4 g^2) = (1)/(16) ((u^2 sin 2 theta)/( g))^2`
`rArr 16h_1 h_2 = R^2 rArr R = 4 sqrt(h_1 h_2)`.