A projectile is fired into the air at a nonzero angle with the horizontal. When the projectile reaches its maximum height, the speed of the projectile is 21.5% of its original speed. What angle was the projectile originally fired at?

77.58°

Explanation:

Let the projectile is projected at an angle θ and the velocity of projection is u.

At the maximum height, the projectile has only horizontal component of velocity.

Let the velocity at maximum height is v.

According to the question, the velocity at maximum height is 21.5% of initial velocity.

v = 21.5 % of u

u Cos θ = 21.5 % of u

u Cos θ = 0.215 u

Cos θ = 0.215

θ = 77.58°

Thus, the angle of projection is 77.58°.