The body was thrown vertically down from a height of 150 m at a speed of 30 m / s.

The body was thrown vertically down from a height of 150 m at a speed of 30 m / s. How long and with what speed will the body fall to the Earth?

Given:

H = 150 meters – the height from which the body was thrown;

V0 = 30 m / s – initial velocity of the body;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to find the time t (seconds) after which the body will fall to the ground, as well as the speed when falling V (m / s).

According to the equation of motion:

V0 * t + g * t ^ 2/2 = H

30 * t + 5 * t ^ 2 = 150

5 * t ^ 2 + 30 * t – 150 = 0

t ^ 2 + 6 * t – 30 = 0

D = √ (6 ^ 2 + 4 * 30) = 12.5

t1 = (-6 + 12.5) / 2 = 3.25 s; t2 = (-6 – 12.5) / 2 = -9.25 s (t2 does not fit according to the problem statement).

V = V0 + g * t1 = 30 + 10 * 3.25 = 30 + 32.5 = 62.5 m / s.

Answer: the body will fall to the ground in a time equal to 3.25 seconds at a speed of 62.5 m / s when falling.