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.
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.
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