Find the angle of projection at which horizontal range and maximum height are equal.

Explanation

Horizontal range `=(u^(2)sin theta)/(g)`
Maximum height attained `=(u^(2) sin^(2) theta)/(2g)`
`(u^(2) sin2theta)/(g)=(u^(2)sin^(2) theta)/(2g)`
`rArr (u^(2)2sin theta cos theta)/(g)=(u^(2) sin theta sin theta)/(2g)`
`rArr (u^(2)2sin theta cos theta)/(g) =(u^(2) sin theta sin theta)/(2g)`
`4=tan theta`
`4=tan theta`
`theta=tan ^(-1)(4)`