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

Answer

D

Explanation

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