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 ?

Options

A. `R = (sqrt(h_1 h_2))`
B. `R = (sqrt(2 h_1 h_2))`
C. `R = 2 sqrt(h_1 h_2))`
D. `R = 4 sqrt(h_1 h_2))`

Answer

D

Explanation

(d) Range is same for angles of projection `theta and 90^@ - theta`,
`R = (u^2 sin^2 theta)/(g), h_1 = (u^2 cos^2 theta)/(2 g)`
and `h_2 = (u^2 sin^2 (90 - theta))/(2 g) = (u^2 cos^2 theta)/(2 g)`
Hence, `(sqrt(h_1 h_2)) = (u^2 sin theta cos theta)/(2 g) = (1)/(4) [(u^2 sin 2theta)/(g)] = (R)/(4)`.