Consider the initial vertical component of the velocity is .

The vertical acceleration of the projectile is .

The velocity of the projectile is .

Vertical velocity of the projectile when it reaches the maximum height is .

.

.

The time taken by projectile to reach the maximum height is .

The distance travelled by the projectile is .

Substitute .

.

The height reached by projectile in half the time required to reach the maximum height is

.

substitute .

.

Therefore, a projectile reaches three quarters of its maximum height in half the time needed to reach its maximum height.

A projectile reaches three quarters of its maximum height in half the time needed to reach its maximum height.