At what speed should the ball be thrown down from a height of 3 meters

At what speed should the ball be thrown down from a height of 3 meters so that it jumped to a height of 8 meters. the impact of the ball is absolutely elastic.

Given:

h1 = 3 meters – initial height of the ball;

h2 = 8 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.

According to the condition of the problem, the impact of the ball on the surface is absolutely elastic, that is, energy losses can be ignored. 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 * (8 – 5)) 0.5 = (2 * 10 * 3) 0.5 = (20 * 3) 0, 5 = 600.5 = 7.7 m / s (result rounded to one decimal place).

Answer: The ball must be thrown at a speed of 7.7 m / s.