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Estimating variable velocity with a computer model
Let's write a script that approximates the graphic procedure that I described earlier.
Please copy the code from Listing 2 into an html file and open the file in your browser.
| Listing 2 . Variable velocity exercise #2. |
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<!---------------- File JavaScript2.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script</br>");
//Declare and initialize constantsvar g = -32.2;//acceleration of gravity in ft/sec/sec
var v0 = 100;//initial velocity in ft/secvar h0 = 6;//initial height in feet
var tInc = 0.25;//calculation interval in seconds//Declare and initialize working variables
var t = .0001;//current time in secondsvar h = h0;//current height in feet
var v = 0;//current velocity in feet/secvar oldT = 0;//previous time in seconds
var delT = 0;//change in time in secondsvar oldH = h0;//previous height in feet
var delH = 0;//change in height in feet//The following variable is used to insert spaces in
// the output display.var sp = " "
//Compute and display various values for as long as the// height of the projectile is above the ground.
while(h>0){
//This is the general equation for the height of a// projectile under the influence of gravity in a
// vacuum.h = h0 + v0*t +0.5*g*t*t;
//Compute and save the time interval since the// previous estimate of height, etc.
delT = t-oldT;oldT = t;//Save the current time for the next iteration
//Estimate the velocity based on the change in// height since the previous estimate.
delH = h-oldH;v = delH/delT;//compute velocity
oldH = h;//Save the current height for the next iteration.//Display the information for this iteration
document.write("t = " + t.toFixed(2) + " seconds" + sp +" h = " + h.toFixed(1) + " feet" + sp +
" v = " + v.toFixed(2) + " feet/second" + sp +"</br>");
//Increment the time for the next iteration.t = t + tInc;
}//end while loopdocument.write("End Script");</script></body></html> |
Screen output
The text shown in Figure 6 should appear in your browser window when the html file opens in your browser.
| Figure 6 . Screen output for Listing #2. |
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Start Script
t = 0.00 seconds h = 6.0 feet v = 100.00 feet/secondt = 0.25 seconds h = 30.0 feet v = 95.97 feet/second
t = 0.50 seconds h = 52.0 feet v = 87.92 feet/secondt = 0.75 seconds h = 72.0 feet v = 79.87 feet/second
t = 1.00 seconds h = 89.9 feet v = 71.82 feet/secondt = 1.25 seconds h = 105.8 feet v = 63.77 feet/second
t = 1.50 seconds h = 119.8 feet v = 55.72 feet/secondt = 1.75 seconds h = 131.7 feet v = 47.67 feet/second
t = 2.00 seconds h = 141.6 feet v = 39.62 feet/secondt = 2.25 seconds h = 149.5 feet v = 31.57 feet/second
t = 2.50 seconds h = 155.4 feet v = 23.52 feet/secondt = 2.75 seconds h = 159.2 feet v = 15.47 feet/second
t = 3.00 seconds h = 161.1 feet v = 7.42 feet/secondt = 3.25 seconds h = 160.9 feet v = -0.63 feet/second
t = 3.50 seconds h = 158.8 feet v = -8.68 feet/secondt = 3.75 seconds h = 154.6 feet v = -16.73 feet/second
t = 4.00 seconds h = 148.4 feet v = -24.78 feet/secondt = 4.25 seconds h = 140.2 feet v = -32.83 feet/second
t = 4.50 seconds h = 130.0 feet v = -40.88 feet/secondt = 4.75 seconds h = 117.7 feet v = -48.93 feet/second
t = 5.00 seconds h = 103.5 feet v = -56.98 feet/secondt = 5.25 seconds h = 87.2 feet v = -65.03 feet/second
t = 5.50 seconds h = 69.0 feet v = -73.08 feet/secondt = 5.75 seconds h = 48.7 feet v = -81.13 feet/second
t = 6.00 seconds h = 26.4 feet v = -89.18 feet/secondt = 6.25 seconds h = 2.1 feet v = -97.23 feet/second
t = 6.50 seconds h = -24.2 feet v = -105.28 feet/secondEnd Script |
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