Abstract
The purpose of this lab was to find the initial velocity of an angled projectile. Values of the experiment such as; the vertical and horizontal displacement and the angle at which it was projected were measured, and then used in the calculation of the initial velocity of the projectile.
IntroductionThis lab explored the procedure in which there are only a few variables of the experiment given and a result for another value must be calculated. In the case of this lab, an arrow was launched at an angle (making it an angled projectile) and the displacement that the arrow had and the angle at which the arrow was projected at, were both measured. A projectile is when there is both vertical and horizontal motion, and those two values are independent from each other and are therefor analyzed separately. Though they represent the motion of the same object they have different values such as; the vertical motion will always accelerate downwards due to the gravity and the horizontal motion will always have a constant velocity with no acceleration.
HypothesisIf given an angle, the vertical height, the horizontal displacement and the vertical acceleration, then it is possible to calculate the initial velocity of an angled projectile.
MaterialsPen or pencil |
ProcedureAfter assembling the projectile launcher and loading an arrow onto it, the power was set to the eighth setting and the angle to 45 degrees. The measuring tape was secured from the point on the table directly below the end of the launchers pole, using masking tape. The measuring tape was then extended to about 2.5 meters away from the tip of the point. The slow- motion camera was placed along the measuring tape so that it would be able to capture approximately 50 cm of the arrows displacement, so it was set up with the expectations to film from the 175 cm mark to the 125 cm mark. The camera began filming slightly before each arrow was projected and then after each trial the camera footage was used to find where the dart initially reached the table and each result was recorder. Then a pencil or a pen was used to fix the opening in the arrow as it was damaged and closed each time it landed. The arrow was launched 10 successful times and recorded after each individual trial. Using the data that was measured the average horizontal displacement was found and then used along with the other known values (vertical displacement, vertical acceleration and the angle) the initial velocity was calculated using the equations below.
EquationsDATA and AnalysisTable 1: Horizontal Displacement
Table 2: Independent/ Controlled Variables
Each measurement for the horizontal displacement was relatively consistent to the others, averaging at 1.97m.
Videos of trialsIn this experiment the variables such as; the angle, the power setting, the vertical displacement and horizontal displacement are the independent/controlled values. The initial velocity depends on the those values and therefore makes it the dependent value.
DiscussiontThis purpose of this lab was to calculate the initial velocity of an angled projectile when only given a few variables. The hypothesis that was created before the experiment was proven to be a correct statement as the initial velocity of the projected arrow was solved for. Before it was possible to solve for the initial velocity more information and variables had to be measured, including horizontal displacement, vertical displacement, the angle and power setting of choice. With these variables known and an equation to use, the initial velocity was calculated and recorded. After all calculation the initial velocity was 3.71 m/s, which was neither a surprise or a expected, as it is difficult to judge the speed of an object as it flys through the air for only a few seconds. Most aspects and results of this experiment were expected to happen in the way that it did, except for the horizontal distance. Set at a high power level the experimenters thought that because of the level of power that the horizontal displacement would have been larger then what it actually was. However the fact that the horizontal displacemnt stayed so close in range was expected, each trial the displacment remained between 1.77 meters and 2.22 meters. Besides this unexpected result, the rest of the experiment went as expected.
Sources of errorThroughout this lab a few experimental errors occurred that effected that calculated results. Firstly, the exact location of where the arrow landed each trial was difficult to determine. Though a slow motion video camera was used to help with this, it was still extremely difficult to pin point exactly the measurement of the impact.
Another source of error was unexpectedly found in the arrow itself. Each trial that the arrow endured, the tip if the arrow would be rushed and dull the point. Though after every trial was complete an experimenter would try and reform the tip it would never be back to its original shape. This malformed arrow resulted in friction increasing from the pole and the arrow as it tried to slide off, potentially effecting the results that were later calculated. Finally air resistance creates a source of error. As each trial took place the arrow would experience air resistance as it would shoot off the slingshot, once again potentially influencing the data as this factor was not accounted for. |
Further Research
For further research on the topic of angled projectiles, another experiment could take place comparing different angles and power levels to others. This would then give evidence to how each variable effects the others and how angled projectiles function.