Two projectiles `A` and `B` are thrown from the same point with velocities `v` and `v/2` respectively. If `B` is thrown at an angle `45^(@)` with horizontal.What is the inclination of `A`.when their ranges are the same?

Options

A. `sin^(-1) ((1)/(4))`
B. `(1)/(2)sin^(-1) ((1)/(4))`
C. `2 sin^(-1) ((1)/(4))`
D. `(1)/(2) sin^(-1)((1)/(8))`

Answer

D

Explanation

Given, `R_(A) = R_(B)`
`rArr (v^(2) sin2 theta)/(g) = ((v//2)^(2) sin 90^(@))/(g)`
`rArr sin 2 theta = (1)/(4)` or `theta = (1)/(2) sin^(-1) ((1)/(8))`
`:. theta = (1)/(2) sin^(-1)((1)/(8))`