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

Answer

B

Explanation

(b): For a given speed of projection range is found to be same for two angles `theta` and `90^(@)- theta` .
`R=(u^(2) sin 2theta)/(g)`
`rArr h_(1)=(u^(2) sin ^(2) theta)/(2g)`
`rArr h_(2)=(u^(2) sin ^(2) (90-theta))/(2g)=(u^(2) cos ^(2) theta)/(2g)`
`rArr sqrt(h_(1)h_(2))=(u^(2))/(2g) sin theta cos theta=(u^(2) sin 2theta)/(4g)`
`rArr (u^(2) sin 2theta)/(g)=4sqrt(h_(1)h_(2))`
`rArr R=4 sqrt(h_(1)h_(2))`
Hence, option (b) is correct .