A projectile has a range of 50 m and reaches a maximum height of 10m . Calculate the angle at which the projectile is fired .

Explanation

Here R = 50 m, H = 10m , `theta` = ?
` R = (u^(2) sin 2 theta)/(g)`
`= (2u^(2) sin theta cos theta)/(g) " " . . . (1)`
Maximum height,
`H = (u^(2) sin^(2) theta)/( 2g) " ". . . (2)`
Dividing (2) by (1) , we get
`(H)/(R) = (u^(2) sin^(2) theta)/( 2g) xx (g) / (2 u^(2) sin theta cos theta)`
`= (1)/(4) tan theta`
(or) `tan theta = (4H)/(R) = (4 xx 10)/(50) = 0 . 8`
(or) `theta = tan^(-1) (0.8) = 38 . 66^(@)`