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## Energy due to Gravity of Objects Projected Downward

by Ron Kurtus (revised 2 October 2013)

When an object at some height in projected downward and released, its initial velocity becomes a factor in its kinetic energy (**KE**) but does not affect its potential energy (**PE**).

You can calculate the **PE**, **KE** and total energy (**TE**) for an object that is thrown downward with some simple equations. You can then verify that the final velocity is the same as obtained from the gravity derivations.

Questions you may have include:

- Is the potential energy dependent on the kinetic energy?
- What is the initial and final energy for an object thrown downward?
- What is the energy and final velocity for an object projected downward?

This lesson will answer those questions. Useful tool: Units Conversion

## Potential energy of object

The potential energy (**PE**) of an object projected downward is independent of its velocity. It is only dependent of the height above the ground.

Initial and final PE and KE

Thus, the initial **PE** is:

PE_{i}= mgh

The final potential energy is:

PE0_{f}=

The potential energy of the object is independent on its kinetic energy.

## Kinetic energy when projected downward

The initial kinetic energy of an object projected downward is dependent on its initial velocity:

KE_{i}= mv_{i}^{2}/2

where

**KE**is the initial kinetic energy in joules (J) or foot-pounds (ft-lbs)_{i}**v**is the initial velocity of the object in m/s or ft/s_{i}

The object accelerates until it hits the ground at a final **KE**:

KE_{f}= mv_{f}^{2}/2

## Total energy and final velocity

The total energy relationship is:

PE_{i}+ KE_{i}= PE_{f}+ KE_{f}

mgh + mv0_{i}^{2}/2 =+ mv_{f}^{2}/2

Divide by **m**, multiply by 2 and rearrange terms to get the final velocity:

v_{f}^{2}= 2gh + v_{i}^{2}

v_{f}= √(2gh +v)_{i}^{2}

This equation corresponds with the equation from Velocity Equations for Objects Projected Downward:

v = √(2gy +v)_{i}^{2}

where **y** is the displacement below the starting point.

## Summary

Potential energy with respect to gravity is **PE = mgh**. When the object is dropped, thrown downward or projected upward, its kinetic energy becomes **KE = mv ^{2}/2**, along with a factor of the initial velocity.

The sum of the **PE** and **KE** is the total energy, which is a constant. Equating the initial total energy with the final total energy, you can determine the final velocity of the object.

Gain confidence through small successes

## Resources and references

### Websites

**Gravity and Potential Energy** - University of Alaska

### Books

**Top-rated books on Simple Gravity Science**

**Top-rated books on Advanced Gravity Physics**

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