Physics

To solve this problem, we need to find the height at which the ball's kinetic energy (KE) is equal to its potential energy (PE) during its upward motion.

 

Define the initial conditions

The ball is thrown vertically upward with an initial speed of . The initial kinetic energy is:

At the initial height (which is for simplicity), the potential energy is:

 

General expressions for KE and PE at height

At some height , the potential energy is:

The kinetic energy is given by:

 

We know that the total mechanical energy at any point is the sum of kinetic and potential energy, and it must remain constant (since there is no air resistance). The total mechanical energy is the sum of the initial KE and initial PE: