Determine the speed of the body at a height of 72m, if it is thrown upwards at a speed of 20m / s?

Given:

V0 = 20 m / s – the speed with which the body is thrown vertically upward;

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

H = 72 meters – height.

It is required to determine the speed of the body V (m / s) at the height H.

Let us find the time it takes for the body to rise to the height H:

H = V0 * t – g * t ^ 2/2;

20 * t – 10 * t ^ 2/2 = 72

-5 * t ^ 2 + 20 * t – 72 = 0

5 * t ^ 2 – 20 * t + 72 = 0

t ^ 2 – 4 * t + 14.4 = 0

D = 4 ^ 2 – 4 * 14.4 = 16 – 57.6 = -41.6.

Since the discriminant of the quadratic equation is negative, the equation has no solution. Physically, this means that the body will not reach a height of 75 meters.

Answer: the body will not reach a height of 75 meters, so we can assume that the speed will be zero.