Question

If the greatest height attained by a projectile be equal to the horizontal range, then the angle of projection is

Options

• `tan^-1  1/4`

• `tan^-1 4`

• `tan^-1 2`

• `tan^-1 2sqrt(2)`

Answer 1

`tan^-1 4`

Explanation:

According to question

H = R

⇒ `(4^2 sin^2 theta)/(2g) = (mu^2 sin 2theta)/g`

⇒ sin²θ = 2 sin²θ

⇒ sin²θ = 4 sin θ . cos θ = 0

⇒ sin θ - 4 sin θ . cos θ = 0

⇒ sinθ[sin θ – 4 cos θ] = 0

∵ sin θ = 0

∴ sin θ – 4 cos θ = 0

tan θ 4 ⇒ θ = tan^–14.