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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 14 should appear in your browser window when you open the html file in your browser.

Figure 14 . 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 14 . 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 14 .

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 results document.write("Arrow reaches maximum height of " +h.toFixed(2) + " feet " + "</br>"); document.write("</br>End Script");</script></body></html>

Questions & Answers

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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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