Question

The potential energy of a projectile at its maximum height is equal to its kinetic energy there

Answer 1

We have the expression for maximum height,

h = u² sin²θ / 2g

At maximum height, v = u cosθ. Because the x component of v is u cosθ where the y component is 0.

Let the mass of the projectile be m.

Given that the potential energy at maximum height is equal to the kinetic energy, i.e.,

m g h = m v² / 2

m g u² sin²θ / 2g = m u² cos²θ / 2

sin²θ = cos²θ

Since θ is acute,

sinθ = cosθ => tanθ = 1

This implies θ = 45°