<< Chapter < Page Chapter >> Page >

h = v0*t + 0.5*g*t^2

where

  • h is the distance of the projectile above the surface of the earth in units of distance
  • v0 is the initial velocity of the projectile in units of distance/time
  • t is time in seconds
  • g is the acceleration of gravity, approximately 9.8 meters per second squared, or approximately 32.2 feet per second squared.

Some physics textbooks also list the following equations as being important .

v = v0 + g*t

v^2 = v0^2 + 2*g*h

where v is the velocity of the object and the other terms are the same as described above .

Exercise to find the velocity

Let's do an exercise using the first of the two equations given above .

An individual on the surface of the earth shoots an arrow directly upward with a velocity of 100 feet per second. How many seconds elapse before the arrow turns and starts falling towards thesurface of the earth. Ignore the effects of air resistance.

Create a script

Please copy the code from Listing 6 into an html file and open the file in your browser.

Listing 6 . Exercise to find the velocity.
<!---------------- File JavaScript06.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script<br/><br/>"); //Initialize the problem parameters.var g = -32.2;//gravity in ft/sec*sec on Earth var v0 = 100;//initial velocity in ft/sec//Given that v = v0 + g * t //At what time does the velocity go to zero?//Rearrange the terms in the equation. var t = -v0/g;//Display the results document.write("Arrow has zero velocity at " +t.toFixed(2) + " seconds " + "<br/>"); document.write("<br/>End Script");</script></body></html>

Screen output

The text shown in Figure 10 should appear in your browser window when you open the html file in your browser.

Figure 10 . Screen output for Listing #6.
Start Script Arrow has zero velocity at 3.11 secondsEnd Script

Analysis of the code

Compared to working through the solutions to the previous exercises, this one seems almost trivial.

After establishing values for the acceleration of gravity and the initial velocity of the arrow, the code in Listing 6 rearranges the first equation given above and solves for the value of time at which the velocity goes to zero. This is the point in time when the arrow turnsfrom moving up and begins falling back toward the earth.

The results are shown in Figure 10 . You should compare this result with Figure 1 , which shows that the arrow reaches its maximum height at approximately 3 seconds, which agrees very well with the result shown in Figure 10 .

Exercise to find the height

Let's do an exercise using the second of the two equations given above .

An individual that is six feet tall standing on the surface of the earth shoots an arrow directly upward with a velocity of 100 feet per second. What is the maximum height achieved by the arrow before it turns and falls backtowards the surface of the earth? Ignore the effects of air resistance.

Create a script

Please copy the code from Listing 7 into an html file and open the file in your browser.

Listing 7 . Exercise to find the height.
<!---------------- File JavaScript07.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script<br/><br/>"); //Initialize the problem parameters.var g = -32.2;//gravity in ft/sec*sec on Earth var v0 = 100;//initial velocity in ft/secvar h0 = 6;//initial height //Given that v^2 = v0^2 +2*g*h //What is the maximum height reached by the arrow?//Note that the maximum height is six feet more than // the value given by the above equation because that// equation is based on the point of release. //The maximum height occurs when the velocity goes to zero.//Setting the velocity to zero and rearranging the terms // in the equation gives:var h = h0 + (-(v0 * v0))/(2*g); //Display the resultsdocument.write("Arrow reaches maximum height of " + h.toFixed(2) + " feet " + "<br/>"); document.write("<br/>End Script");</script></body></html>

Screen output

The text shown in Figure 11 should appear in your browser window when the html file is opened in your browser.

Figure 11 . Screen output for Listing #7.
Start Script Arrow reaches maximum height of 161.28 feetEnd Script

Analysis of the code

Once again, compared to working through the previous exercises, this one also seems almost trivial.

After establishing values for the acceleration of gravity, the initial velocity of the arrow, and the height at which the arrow was released, the code in Listing 7 rearranges the second equation given above and solves for the value of the height (relative to the release point) at which the velocity goes to zero. This is the pointin the trajectory where the arrow turns from moving up and begins falling back toward the earth.

Note that in order to get the actual height, it was necessary to add the initial height of 6 feet to the computed height.

Compare the results

The results are shown in Figure 11 . You should compare this result with Figure 2 , which shows that the arrow reaches its maximum height at approximately 161.1 feet, which agrees very well with the result shown in Figure 11 .

Run the scripts

I encourage you to run the scripts that I have presented in this lesson to confirm that you get the same results. Copy the code for each script into atext file with an extension of html. Then open that file in your browser. Experiment with the code, making changes, and observing the results of your changes. Makecertain that you can explain why your changes behave as they do.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: GAME 2302 Motion -- Variable Velocity and Acceleration
  • File: Game0380.htm
  • Published: 10/13/12
  • Revised: 02/01/16
Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDFfile for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware thatsome of the HTML elements in this module may not translate well into PDF.

I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.comshowing me as the author. I neither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, pleasebe aware that it is a copy of a module that is freely available on cnx.org and that it was made and published without my prior knowledge.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Game 2302 - mathematical applications for game development' conversation and receive update notifications?

Ask