An object is projected at an angle θ into the atmosphere using a complex mechanism. The projectile travels with a specific velocity 'u' and makes an angle θ with the horizontal plane. In order for the projectile to travel maximum distance, the value of θ should be

An object is projected at an angle θ into the atmosphere using a complex mechanism. The projectile travels with a specific velocity 'u' and makes an angle θ with the horizontal plane. In order for the projectile to travel maximum distance, the value of θ should be Correct Answer 45⁰

The resistance offered by air to the movement of projectile is neglected.

The maximum distance travelled by projectile is given by

R = (u² sin 2θ)/g

where g is acceleration due to gravity.

In the above formula the initial height of projectile is not considered. It is assumed that the projectile is launched from a flat ground.

For the specific velocity 'u', R is maximum when sin 2θ = 1

This implies 2θ = 90⁰ ⇒ θ = 90⁰/2 = 45⁰