At what speed is it necessary to throw the ball vertically from a height of 5m so that after hitting

At what speed is it necessary to throw the ball vertically from a height of 5m so that after hitting the ground it would jump to a height of 7.5m?

Given:

h1 = 5 meters – initial height of the ball;

h2 = 7.5 meters – required ball height;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine v (meter per second) – with what speed you need to throw the ball down.

Since the condition of the problem is not specified, we consider the impact of the ball on the ground to be absolutely elastic, that is, we do not take into account the loss of energy. Then, according to the law of conservation of energy:

Ekin1 + Epot1 = Epot2;

m * v ^ 2/2 + m * g * h1 = m * g * h2, where m is the mass of the ball;

v ^ 2/2 + g * h1 = g * h2;

v ^ 2/2 = g * h2 – g * h1;

v ^ 2/2 = g * (h2 – h1);

v ^ 2 = 2 * g * (h2 – h1);

v = (2 * g * (h2 – h1)) ^ 0.5 = (2 * 10 * (7.5 – 5)) ^ 0.5 = (2 * 10 * 2.5) ^ 0.5 = (20 * 2.5) ^ 0.5 = 50 ^ 0.5 = 7.1 m / s (the result is rounded to one decimal place).

Answer: The ball must be thrown at a speed of 7.1 m / s.