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Overview of Gravity Equations for Objects Projected Upward
by Ron Kurtus (revised 7 August 2010)
When you throw or project an object upward, its initial velocity is considered a negative number or less than zero (vi < 0).
Note: The convention we use for the direction of the velocity is that a downward velocity is positive and an upward velocity is negative. Also, the distance above the starting point is negative and below is positive.
Some textbooks consider up as positive and down as negative. We feel it is more logical to consider an object that is accelerating downward to have a positive velocity. However, you need to be aware of what convention is being used when working from a book.
(See Convention for Gravity Direction for more information.)
The object moves upward, slowing down from its initial velocity until it reaches its peak or maximum height. Then the object falls toward the ground. Knowing the initial velocity, you can calculate the velocity, distance and time of the object during its flight.
This lesson is an overview of the equations and has references to the other lessons that provide the details.
Questions you may have include:
- What are the equations for velocity?
- What are the equations for distance?
- What are the equations for time?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Velocity equations
The equations for the velocity of an object projected upward at an initial velocity of vi are:
With respect to time
v = gt + vi
With respect to distance
v = −√(2gy + vi2) (going up)
vm = 0 (at maximum height)
v = +√(2gy + vi2) (coming down)
(See Gravity Velocity Equations for Objects Projected Upward for details.)
Distance equations
The equations for the distance from the starting point of an object projected upward at an initial velocity of vi are:
With respect to velocity
y = (v2 − vi2)/2g
ym = −vi2/2g (distance to peak or maximum height)
With respect to time
y = gt2/2 + vit
(See Gravity Distance Equations for Objects Projected Upward for details.)
Time equations
The equations for the time an object projected upward at an initial velocity of vi travels are:
With respect to velocity
t = (v − vi)/g
With respect to distance
t = [−vi − √(vi2+ 2gy)]/g (going up)
tm = −vi/g (time to reach maximum height)
t = [−vi + √(vi2+ 2gy)]/g (coming down)
(See Gravity Time Equations for Objects Projected Upward for details.)
Summary
When you project an object upward, its equations for velocity, distance and time depend on the direction of motion and position above or below the starting point.
We consider upward velocity to be negative and downward to be positive. Likewise, distances above the starting point are negative and below are positve numbers.
See the Side Menu for more Gravity and Gravitation topics
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Resources
The following resources provide information on this subject:
Websites
Acceleration due to Gravity Calculations - from Western Washington University
Gravity and Gravitation Resources
Books
Top-rated
books on Simple Gravity Science
Top-rated
books on Advanced Gravity Physics
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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Overview of Gravity Equations for Objects Projected Upward