# The ball is thrown vertically up to a height of 10 m. Find the speed of the ball at the moment

The ball is thrown vertically up to a height of 10 m. Find the speed of the ball at the moment when the kinematic energy is equal to the potential.

Given:

H = 10 meters – the height at which the ball was thrown;

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

It is required to determine v (m / s) – the speed of the ball at the moment when the kinetic energy is equal to the potential energy.

At maximum height, the ball will only have potential energy W1. Then, according to the law of conservation of energy:

W1 = E2 + W2 – where E2 and W2 are the kinetic and potential energy of the body at a certain height.

Since by the condition of the problem E2 = W2, then:

W1 = 2 * E2;

m * g * H = 2 * m * v ^ 2/2;

g * H = v ^ 2;

v = (g * H) ^ 0.5 = (10 * 10) ^ 0.5 = 100 ^ 0.5 = 10 m / s.

Answer: the speed of the body will be equal to 10 m / s.

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