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^(2)=4h_(1)h_(2)`
B. `R^(2)=2h_(1)h_(2)`
C. `R^(2)=h_(1)h_(2)`
D. `R^(2)=16h_(1)h_(2)`

Answer

D

Explanation

Two angles of projection are `alpha` and `beta`
Range is equal `toalpha+beta=90^(@)`
`h_(1)h_(2)=((u^(2)sin^(2)alpha)/(2g))((u^(2)sin^(2)beta)/(2g))=(u^(4)sin^(2) alpha cos^(2)alpha)/(4g^(2))=(u^(4)sin^(2) 2 alpha)/(16g^(2))=1/16 ((u^(2)sin 2alpha)/g)^(2)=(R^(2))/16impliesR^(2)=16 h_(1)h_(2)`