What is the lowest safe flight altitude over the range if the initial velocity of the projectile is 800

What is the lowest safe flight altitude over the range if the initial velocity of the projectile is 800 m / s and the shooting is carried out at an angle of 15 degrees.

V0 = 800 m / s.

∠α = 15 °.

g = 9.8 m / s2.

h -?

The lowest safe flight altitude should be higher than the height of the projectile above the ground h.

The movement of the projectile can be divided into two types: horizontally, it moves uniformly with a speed Vx = V0 * cosα, vertically uniformly accelerated with gravitational acceleration g and an initial speed V0у = V0 * sinα.

The projectile moves vertically until it stops completely, at the maximum height h its vertical component of velocity will be Vу = 0.

h = (V0y ^ 2 – Vy ^ 2) / 2 * g.

h = V0у ^ 2/2 * g = (V0 * sinα) ^ 2/2 * g.

h = (800 m / s * sin15 °) ^ 2/2 * 9.8 m / s2 = 2173.5 m.

Answer: the lowest safe flight altitude above the range is h = 2173.5 m.