Question

Prove that for a projectile fired from level ground at an angle `theta` above the horizontal, the ratio of the maximum height H to the range R is given by
`(H)/(R)=(1)/(4)tan theta`

Answer 1

`H=(u^(2)sin ^(2)theta)/(2g)` and `R=(u^(2)sin2 theta)/(g)`
`(H)/(R)=(sin ^(2)theta)/(2sin 2theta)=(sin^(2)theta)/(4sin theta cos theta)=(1)/(4) tan theta`