The relation between kinetic and potential energy

The potential energy is the energy accumulated in an object by its location.

PE = mgh where, m - mass, g - acceleration due to gravity and h - height

The energy possessed by an object as a result of its motion is known as kinetic energy.

KE KE = \frac{1}{2} mv^2   Where, m-mass and v- velocity  

Energy cannot be destroyed, only converted from one form to another, according to the law of conservation of energy.

PE begins from 0 at the projection point and increases to a maximum value at a constant speed at maximum height.

KE begins at the projection point with a maximum value and decrease constantly to 0 at maximum height.

Total energy = PE + KE.

At the maximum height (when object dropped): PE = KE

Step 1: Set up an equation for the height

Given that

Mass of rock m = 0.2 kg

Speed of the stone v = 5 m/s   

Acceleration due to gravity a = 9.8 m/s^2   

Kinetic energy = Potential energy

PE = PE .

mgh = \frac{1}{2} mv^2

h = \frac{1}{2} \frac{v^2}{g}

Step 2: determining the height reached by the stone

h = \frac{1}{2} \frac{(5 m/s)^2}{(9.8 m/s^2)}

h = \frac{25}{2*9.8} = 1.27

Hence, height reached by the stone = 1.27 m

Since the kinetic energy is equal to the potential energy at the maximum height,

mgh = \frac{1}{2} mv^{2}

h=\frac{1}{2}\left(\frac{v^2}{g}\right)

h=0.5\left(\frac{25\ \frac{m^2}{s^2}}{9.8\ \frac{m}{s^2}}\right)\approx1.27\ m

The height of the stone will be 1.27 m.