| << Chapter < Page | Chapter >> Page > |
Analysis of the output
Your curve should begin at a height of 6 feet and the height should increase on a point-by-point basis out to about 3 seconds. The maximumheight should occur around 3 seconds and should then start decreasing. The height should go to zero between6.25 seconds and 6.5 seconds.
Not a trip to outer space
As you are probably aware, shooting an arrow upward does not cause the arrow to go into outer space, unless the arrow is self-propelled and manages to reach avelocity commonly known as the "escape velocity."
Instead, for any practical value of initial velocity (neglecting air resistance), gravitational attraction will eventually cause the arrow to slowdown, reverse course, and fall back to earth with continually increasing velocity until it strikes the earth and stops. That is the message conveyed bythe plot of height in Figure 1 and the output from the script shown in Figure 2 .
The maximum height
At about 3 seconds and a height of about 161 feet, the kinetic energy provided by the initial velocity will have been dissipated by the gravitationalattraction of the earth. At that point, the arrow won't go any higher. Instead, it will start falling back toward the earth. Somewhere around 6.25 seconds, itwill strike the earth.
The shape of the curve
The shape of this curve is controlled by only two factors: the initial velocity of the arrow and the gravitational attraction of the earth. The archerhas some degree of control over the initial velocity, but has no control over the gravitational attraction of the earth.
In theory, in the absence of an atmosphere, if the arrow is shot straight up, the arrow should land in the same place from which it was shot. In practice in the real world, wind and other factors wouldprobably prevent that from happening.
Variable velocity
We learned in an earlier module that if velocity is uniform, the displacement should be the same during each successive equal interval oftime. However, we can see from Figure 2 that is not true in this case. For example, Figure 3 shows the displacement versus time for the first five time intervals and we can see that it is anything but uniform.
| Figure 3 . Displacement versus time for first five time intervals. |
|---|
Interval Displacement
1 242 22
3 204 17.9
5 15.9 |
Successively decreasing or increasing displacement
Referring back to Figure 2 (along with Figure 3 ), we see that the displacement during the first 0.25 second time interval was 24 feet, but the displacementbetween 2.75 seconds and 3.0 seconds was only 1.9 feet, Furthermore, the displacement was -0.2 feet during the interval between 3 seconds and 3.25 seconds indicating thatthe arrow had begun falling back to the earth.
As you can see in Figure 2 , from that point until contact with the ground, the displacement increased during each 0.25 second interval.
In this case, the velocity clearly wasn't uniform. Instead it was variable. The velocity decreased as the arrow was going up, and increased as the arrow wasfalling back down.
Notification Switch
Would you like to follow the 'Game 2302 - mathematical applications for game development' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|