Question

Two bodies are projected from ground with same speeds $40\, ms ^{-1}$ at two different angles with respect to horizontal The bodies were found to have same range If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ____$m$ (Given $g=10 ms ^{-2}$ )

Hint:

The maximum height attained by a projectile depends on its initial speed and the sine of the angle of projection.

Answer 1

Correct Answer: 80

The correct answer is 80.

Answer 2

For projectile motion, the maximum height attained by a projectile is given by: \[ H = \frac{v^2 \sin^2 \theta}{2g} \] The maximum height for the two projectiles, which are projected at angles \( 60^\circ \) and \( 30^\circ \), is: \[ H_1 = \frac{40^2 \sin^2 60^\circ}{2 \times 10} = \frac{1600 \times \left( \frac{\sqrt{3}}{2} \right)^2}{20} = 40 \, \text{m} \] \[ H_2 = \frac{40^2 \sin^2 30^\circ}{2 \times 10} = \frac{1600 \times \left( \frac{1}{2} \right)^2}{20} = 20 \, \text{m} \] The sum of the maximum heights is: \[ H_{\text{total}} = H_1 + H_2 = 40 + 20 = 80 \, \text{m} \]