**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 = \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: Finding the final velocity of the stone above the ground

Given that

Mass of the stone m = 50 kg

Height of the stone h = 100 m

Acceleration due to gravity g = 10 m/s^2

Initial velocity u = 0. m/s

Final velocity at the bottom v

Going to find the final velocity using the 3rd motion equation

v^2 - u^2 = 2gh

v^2 - 0^2 = 2* 10 * 100

v = \sqrt{2000}

v= 44.72 m/s

Step 2: Determining the kinetic energy at the bottom (h = 0)

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

KE = \frac{1}{2} 50 * (44.72)^2

KE = 25* 2000

KE = 50000 Joules

Thus, kinetic energy at the bottom KE = 50000 Joules

b) At h = 100 and h = 50 m, PE = ?

At h = 100 m

PE at the top = KE at the bottom (h = 0 m)

PE at the top = 50,000 joules

At h = 50 m

PE at the top (50m) = mgh = 50 * 10 * 50 = 25000 joules

Hence, Potential energy at the top = 50,000 joules and Potential energy at 50 m = 25000 joules.