A cannon ball has the same range R on a horizontal plane for two angles of projection. If `h_(1)` and `h_(2)` are the greatest heights in the two paths for which this is possible then:

Options

A. `R=h_(1)h_(2)`
B. `R=4sqrt(h_(1)h_(2))`
C. `R=3sqrt(h_(1)h_(2))`
D. `R=(h_(1)h_(2))^(1//4)`

Answer

b

Explanation

`h_(1)=(u^(2)sin^(2)theta)/(2g)`
`h_(2)=(u^(2)sin^(2)(90^(@)-theta))/(2g)=(u^(2)cos^(2)theta)/(2g)`
`h_(1)h_(2)=(u^(2)sin^(2)theta)/(2g)(u^(2)cos^(2)theta)/(2g)`
`=(1)/(16)((u^(2)sin2theta)/(g))^(2)=(R)/(16)`
`therefore R=4sqrt(h_(1)h_(2))`