Background: Projectile motion is a type of two-dimesional motion in which an object or a projectile moves in both the x-direction and the y-direction in a way that creates a generalized parabola shape. This type of motion is often represented as a two-dimensional vector as there is both a magnitude and a direction. It is important to remember when working with projectiles however, that the movement in the x-direction must be treated separately from the movement in the y-direction. It is also important to understand the differences in the accelaration in each direction. In the x-direction, air resistance can often be assumed to be negligible and is therefore represented as 0 m/s2. However, the y-direction must take gravity into account. Assuming the object is on Earth, the accelaration in the y-direction should be -9.8 m/s2. The only variable that overlaps between the x and y-directions when studying projectile motion or other two-dimensional vectors is time, because that measurement is not direction dependant. 

This lab focused on creating a marshmallow shooter and then calculating the initial velocity at which the marshmallow is launched from the shooter. In order to accomplish this objective, a marshmallow slingshot was constructed at a 45 degree angle from the floor using PVC pipes. The marshmallow was then fired and the time it took for it to land on the ground as well as the distance it traveled in the x-direction was measured. Finally, the initial velocities in the x and y directions were able to be calculated using the kinematic equations and the total initial velocity was found using basic trigonometry. 

Equations:

X Initial Velocity = Change in X / Time

Y Initial Velocity = (-Change in Y - (-0.5 x Accelaration x Time^2)) / Time

Total Initial Velocity = Square Root (Change in X^2 + Change in Y^2)

Discussion: The initial velocity of the marshmallow as it exited the marshmallow shooter was determined to be 10.09 m/s with a relative standard deviation of 5.4%. This meant that not only was the marshmallow moving fairly quickly as it left the slingshot, but that the shooter was fairly precise in how quickly it launched the projectile as the standard deviation was less that 10% of the average. There were many steps taken to improve the precision of the marshmallow shooter during the construction process including marking the pull-back string so that the rubber bands were stretched to the same distance every time. The group also made the decision to complete the trials of the marshmallow shooter indoors to avoid any interference from wind or other outside factors that were not being accounted for in the calculations. The Great Room in North Campus Residence Hall was selected for the trials for its size and the ability to move any furniture out of the way of the projectile, and both features were utilized during the launching process. The group also divided which person measured what variable to ensure that there were no inconsistencies in the measurements from person to person. 

Errors: Despite accounting for as many errors as possible during the preparation and construction process, there were still some systematic errors present during the experiment. In addition to reaction time with timing, it was observed during the last few trials that the rubber bands were becoming a little worn. It was determined that changing the rubber bands part-way through the experiment could have had an impact on the results of the study given differences in the strength and lenght of any new rubber bands. Therefore, the bands were not replaced but it was noted that this could have resulted in some inconsistencies in the data.