There are two methods by which this can be solved.
- With the help of Gravitational Potential Energy consideration.
- With the help of Kinetic energy consideration.
I opt for the GPE method.
a. When the ball is thrown upwards from the ground level, its potential energy is zero and it has maximum kinetic energy.
b. As it rises up, the gravity acting against the direction of motion, its velocity decreasing. Part of its kinetic energy gets converted into its potential energy.
c. As it reaches maximum height, its velocity is momentarily zero. At this point all its kinetic energy has been converted in to its potential energy.
Assuming that no energy is lost against air resistance and applying Law of conservation of energy we have
Initial Kinetic Energy