The answer is: 8.62m
<h2>Why?</h2>There are involved two types of mechanical energy: kinetic energy and potential energy, in two different moments.
<h2>First moment:</h2>Before the ball is thrown, where the potential energy is 0.
<h2>Second moment: </h2>After the ball is thrown, at its maximum height, the Kinetic Energy turns to 0 (since at maximum height,the speed is equal to 0) and the PE turns to its max value.
Therefore,
Where:
<em>E</em> is the total energy
<em>PE</em> is the potential energy
<em>KE</em> is the kinetic energy
<em>m</em> is the mass of the object
<em>g</em> is the gravitational acceleration
<em>h </em>is the reached height of the object
<em>v</em> is the velocity of the object
Since the total energy is always constant, according to the Law of Conservation of Energy, we can write the following equation:
Remember, at the first moment the PE is equal to 0 since there is not height, and at the second moment, the KE is equal to 0 since the velocity at maximum height is 0.
So,
Hence,
The height at the second moment (maximum height) is 8.62m
Have a nice day!