Question

A rock at the top of a 30 meter cliff has a mass of 25 kg. Calculate the rock’s gravitational potential energy when dropped off the cliff. Assuming that energy is conserved and there is no air friction and gravity is 9.8 m/sec., at the bottom of the cliff the rock’s potential energy is completely converted to kinetic energy. Use the formula for kinetic energy to calculate the rock’s speed at the bottom of the cliff. Show all calculations.

Answer 1

Potential energy =

                     (mass) x (gravity) x (height above the reference level) .

Relative to the bottom of the cliff, the potential energy
at the top of the cliff is

                         (25kg) x (9.8 m/s²) x (30 meters)

                     =  (25 x 9.8 x 30)  kg-m²/s²

                     =        7,350 joules .

Kinetic energy = (1/2) x (mass) x (speed²)

The rock's kinetic energy at the bottom is
the same as its potential energy at the top.

                                        7,350 joules = (1/2) x (25 kg) x (speed²)

Divide each side
by 12.5kg :                7,350 joules/12.5 kg  =  speed²

                                 7,350 kg-m²/s² / 12.5kg  =  speed²

                                 (7,350 / 12.5)  m²/s²  =  speed²

                                      588 m²/s²  =  speed²
Take the square root
of each side:            
                                   Speed = √(588 m²/s²) 

                                             =  24.248... m/s       (rounded)

Answer 2

Lets see:-

We have our formula for potential energy, which we are trying to solve for, 

PE = mgh  or  potential energy = mass * gravity * height

So we know that PE all depends on these. 

Height :  30 meters
Mass : 25 kg
Gravity (which is always constant) : 9.8 m/s/s

Now add into formula. 

PE = 25*30*9.8 
PE = 7350 Joules

Answer: PE = 7350 Joules