The range of a projectile when launched at angle `theta` is same as when launched at angle `2theta`. What is the value of `theta` ?

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

B

Explanation

Range of projectile launched at an angle `theta` is same as the range of projectile launched at angle `2theta`.
`rArr (u^(2)sin2 theta(2theta))/(g) = (u^(2) sin 2 theta)/(g)`
`rArr sin 2(2theta) = sin 2theta`
`rArr 2 sin 2 theta cos 2 theta = 2 sin theta cos theta`
`4 sin theta cos theta cos 2 theta = 2 sin theta cos theta`
`rArr 4 cos 2 theta = 2 rArr cos2 theta = (1)/(2)`
`rArr cos 2theta = cos 60^(@)`
`rArr 2 theta = 60^(@)`
`rArr theta = 30^(@)`