The ball is thrown horizontally from a height of 15 m. At what initial speed is the ball’s flight range 3 times

The ball is thrown horizontally from a height of 15 m. At what initial speed is the ball’s flight range 3 times the initial height? At what angle to the horizon does the ball move before hitting the ground?

Horizontally, the ball moves uniformly with a speed V0, and vertically – uniformly accelerated, with an acceleration g = 9.8 m / s2.

At the moment the ball falls t1, its height is h = 0, and its range is: L = 3 H = 3 × 15 = 45 m.

L = V0 t1; H = g t1 ^ 2/2; → t1 = L / V0; → H = g L ^ 2 / (2 V0 ^ 2),

whence V0 = [g L ^ 2 / (2 H)] ^ 1/2 = 25.72 m / s.

Components of speed during a fall:

V1х = V0; V1у = g t1 = g L / V0, whence tan α = V1у / V1х = g L / V0 ^ 2.

The desired angle:

α = arctan (g L / V0 ^ 2) = arctan (9.8 × 45 / 25.72 ^ 2) = 33.7o.