SfC Home > Physical Science > Physics >
Explanation of Gravity Distance Equations for Objects Projected Downward - Succeed in Understanding Physics. Also refer to physical science, acceleration, velocity, time, calculation, square-root, Ron Kurtus, School for Champions. Copyright © Restrictions
Gravity Distance Equations for Objects Projected Downward
by Ron Kurtus (28 August 2009)
If you know the initial velocity that an object is thrown or projected downward, you can calculate the distance traveled from the starting point when the object reaches a given velocity or when it reaches a given elapsed time. Some examples illustrate these equations.
The equations were determined from the Derivation of Gravity Equations and are summarized in Overview of Gravity Equations for Objects Projected Downward.
Note: You normally do not need to memorize these equations, but you should know where to find them in order to solve equations.
Questions you may have include:
- How do you find the distance for a given velocity?
- How do you find the distance for a given time?
- What are some examples of these equations?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Distance for a given velocity
If you throw an object downward at some initial velocity, the equation for the distance traveled to reach a given velocity is:
x = (v2 − vi2)/2g
where
- x is the distance from the starting point in meters (m) or feet (ft)
- v is the velocity in meters/second (m/s) or feet/second (ft/s)
- vi is the initial velocity in m/s or ft/s
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
Distance of an object thrown downward as a function of
initial velocity and velocity or time
Distance for a given time
If you throw an object downward, the equation for the distance traveled within a given time is:
x = gt2/2 + vit
where t is the time the object has fallen in seconds (s).
Examples
The following examples illustrate applications of the equations.
For a given velocity
If you throw an object downward at 10 m/s, find the minimum height you must throw it from so that it reaches 50 m/s.
Solution
You are given that vi = +10 m/s and v = 50 m/s. Since vi and v are in m/s,
g = 9.8 m/s2. The equation to use is:
x = (v2 − vi2)/2g
Substitute values in the equation:
x = [(50 m/s)2 − (10 m/s)2]/2*(9.8 m/s2)
x = [(2500 m2/s2) − (100 m2/s2)]/(19.6 m/s2)
x = (2400 m2/s2)/(19.6 m/s2)
x = 122.4 m
For a given time
If you throw an object downward at 30 ft/s and it travels for 4 seconds, find the distance traveled.
Solution
You are given that vi = 30 ft/s and t = 4 s. Since vi is in ft/s, g = 32 ft/s2. The equation to use is:
x = gt2/2 + vit
Substitute values in the equation:
x = [(32 ft/s2)*(4 s)2]/2 + (30 ft/s)*(4 s)
x = (32 ft/s2)*(16 s2)/2 + 120 ft
x = (512 ft)/2 + 120 ft
x = 256 ft + 120 ft
x = 376 ft
Summary
You can calculate the distance traveled from the starting point when an object that is projected downward reaches a given velocity or when it reaches a given elapsed time from the equations:
x = (v2 − vi2)/2g
x = gt2/2 + vit
See the Side Menu for more Gravitation and Gravity topics
Check your numbers
Resources
The following resources provide information on this subject:
Websites
Acceleration due to Gravity Calculations - from Western Washington University
Gravitation and Gravity 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.
What do you think?
Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible.
Share link
Feel free to establish a link from your website to pages in this site.
Or use our form to send this link to yourself or a friend.
Students and researchers
The Web address of this page is:
www.school-for-champions.com/
science/gravity_equations_downward_distance.htm
Please include it as a reference in your report, document, or thesis.
Where are you now?
Gravity Distance Equations for Objects Projected Downward