24-Mar-2015 Trajectories

Purpose

The purpose of this lab was to use what we learned about projectile motion to predict where the ball will land in this experiment. This is done in two parts, the first part is to calculate and find out how fast the ball leaves the v-channel and how long it takes to hit the ground, and the second part is to predict where the ball will hit on a slanted board in front of the v-channel. 

Experiment

The set up for this lab is taking two v-channels and having one on top of the other with one being slanted by a ring stand, then a ball is rolled down the slanted v-channel.  For the first part of the experiment we roll the ball down the slanted v-channel without the slanted board in front of it too see how far the ball will land from the end of the v-channel. We start the ball each time at the same place to ensure we get accurate results and this is done five times. Once all 5 trials are done we measure to see how far the ball went and the height of the table. 

We then take the measurements to find out how long it took for the ball to hit the ground and how fast the ball left the v-channel. V = 1.59 m/s  t = 0.44 s

The second part of the lab where we predict where the ball will land on the slanted board. This is done by taking the the velocity found in the first part and the angle of the board to solve for where the ball will hit the board. We make our prediction then run the experiment just like we did in the first part, except with a board in front of the v-channel at a slant. We also does this five time and then we measure to see how far down the board did the ball hit so we can compare it to our predicted value.We solved for out prediction in the orange in the above picture with D = 0.488 m.

We then then calculate the uncertainty for how far the ball goes down the board by taking partial derivative of the distance function that we came up in the second part. However to make sure it is accurate we substitute in the initial velocity with the initial velocity function from the first part in terms of X and Y. Then the partial derivative is taken in respect with θ, X, and Y which gave us 

D = 0.488 +/- 0.0315 m.

Comparing the predicted and the experimental value we see that they are very close meaning that the model that we came up with and that this experiment was really good for predicting objects trajectory no matter what angle we place the boad at.