0.11 Phy1080: motion -- variable velocity and acceleration  (Page 15/19)

Plot this curve also

Once again, if you are unable to create tactile graphics from the file named Phy1080b1.svg, I recommend that you plot this set of results on top of the previousresults for 45 degrees and compare the two. Which arrow went higher? Which arrow went further along the horizontal axis?

Perhaps you could do the same thing for some other launch angles and determine the launch angle that provides the greatest horizontal range and whichlaunch angle provides the greatest vertical height. How far does the arrow fly when launched at an angle of 0 degrees from a height of 6 feet?

Analysis of the code

The code in this script treats the horizontal and vertical components of motion independently and uses the equation given above to determine the position along that axis as a function of time every 0.25 seconds.

Common parameter values

The code in Listing 4 begins by defining common parameter values for the firing angle, the time increment at which coordinate values will be computed anddisplayed, and the initial velocity of the arrow in the firing direction.

Horizontal and vertical parameters

Following that, the code in Listing 4 defines horizontal parameters and vertical parameters that will be used to compute the horizontal and verticalcomponents of motion respectively.

Horizontal acceleration

The horizontal acceleration is set to zero. In the absence of air resistance, there is nothing to cause the horizontal component of the arrow to speed up orslow down until it stops suddenly when it hits the ground.

Vertical acceleration

The vertical acceleration is set to the acceleration of gravity at the surface of the earth, which is thesame value used for the previous exercises in this module.

Decompose the initial velocity

The cosine and sine functions are used to decompose the initial velocity into horizontal and vertical components of velocity.

Initial horizontal and vertical positions

Finally, the horizontal position when the arrow is released is set to 0 and the vertical position is set to 6 feet, approximately the height of the releasepoint for an archer that is six feet tall.

Working variables

After defining the horizontal and vertical parameters, the code in Listing 4 declares working variables for time, horizontal position (x), and verticalposition (y).

A while loop

A while loop is used to iterate for as long as the arrow is above the ground.

During each iteration, the equation given above is evaluated twice, once to determine the height of the arrow and once to determine the horizontal positionof the arrow at the current time.

Time starts at 0, and increments by +0.25 seconds during each iteration.

The document.write method is called inside the while loop to display the results shown in Figure 8 .

Acceleration of gravity exercise #3

A quadratic equation

Now let's turn things around and approach the problem from a different viewpoint. If we subtract d from both sides of the motion equation given above , replace a by g to avoid confusion later, and then rearrange the terms, we get the following equation :