A cargo for geologists was dropped from a plane flying horizontally.

A cargo for geologists was dropped from a plane flying horizontally. 7 seconds later, he fell to the ground, at a distance from the drop point 4 times the aircraft’s flight altitude. estimate the speed of the aircraft, neglect the air resistance

t = 7 s.

S = 4 * h.

g = 10 m / s2.

V -?

The load is acted upon by the force of gravity m * g, directed vertically downward.

The load will move horizontally uniformly with the aircraft speed V, vertically with the acceleration of gravity g.

The height of the drop of the load h is expressed by the formula: h = g * t ^ 2/2.

h = 10 m / s2 * (7 s) ^ 2/2 = 245 m.

S = 4 * 245 m = 980 m.

The horizontal distance from the place where the load is dropped to its fall l is expressed by the formula: l = V * t.

By the Pythagorean theorem: l = √ (S2 – h2) = √ ((980 m) ^ 2 – (245 m) ^ 2) = 949 m.

V = l / t = 949 m / 7 s = 135.5 m / s.

Answer: the speed of the aircraft is V = 135.5 m / s.