Question

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is `pi/3` and its maximum height is y₁ then the maximum height of the other will be ______.

Options

• 3y₁

• 2y₁

• `y_1/2`

• `y_1/3`

Answer 1

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is `pi/3` and its maximum height is y₁ then the maximum height of the other will be `underlinebb(y_1/3)`.

Explanation:

Let the projection speed be u. For same range the angle of projection are θ and 90° - θ.

∴ Angle of projection in other case

= `pi/2 - pi/3 = pi/6`

∴ In first case, y₁ = `(u^2sin^2  pi/3)/(2g) = 3/4(u^2/(2g))`

In second case, y₂ = `(u^2sin^2  pi/6)/(2g) = 1/4(u^2/(2g))`

Clearly, `y_1 = 3y_2` or `y_2 = y_1/3`