Predicting the Path of a Projectile Motion

1. Ana Leyva, Andrew Imm, Jonathon
The purpose of this experiment was to come up with an equation that would help us predict the point of impact of a projectile motion.
 For this experiment we are trying to calculate the distance that a ball will travel before it hits a wooden plank sitting against a table at a certain angle. In order to calculate this we first have to find the velocity that the ball travels at after it is launched. Then we will use that velocity and the angle to calculate at what distance the ball will hit the board.

We first started off this lab by setting up an apparatus that would allow us to launch the ball. Then we launched the ball to see where it would land on the ground. We then put a piece of carbon paper on top of a white sheet of paper that would allow us to see where the ball is hitting the ground. We then got the average distance from the end of the table to the spot of the ground where the ball hit. We used this distance  and the height of the table to calculate the velocity of the ball when it was launched.

After calculating the initial velocity of the ball we now had to figure out at what distance the ball would hit a plank that was leaning against the table. In order to figure this out we first had to realize that any distance on the plank of wood could be represented as x = dcos(theta) and y = dsin(theta). We then used the equation V_initial *t = dcos(theta) .5gt^2 = dsin(theta) V_initial = 1.53 m/s^2 and theta = 50.0. We then used those equations to solve for d. This d gives us the distance at which the ball is expected to hit. 

 We got the uncertainty in d and v_initial by taking the ln of the v_initial and d equations and then taking the derivative of those two equation. We the plugged in numbers to get the uncertainty in V_initial and d.

My calculation for the distance that the ball would land away from the plank of wood was pretty close but it was less than the distance that I calculated even taking into consideration the propagated uncertainty. The distance I calculated was .8848 m +- 0.00269 with the actual distance being .86m +- 0.1 m. The reason why my distances aren't exact could be because of a calculation error or because my measurements weren't as exact as they could have been. Other than that slight movements of the table and/or apparatus could have also contributed to the differences of the distance