10 September 2014- Trajectories

Purpose: To use our understanding of projectile motion to predict the impact point of a ball on an inclined board.

 This is the set up of order equipment to perform the experiment, where the metal ball land somewhere in the carbon paper on the ground.

This is our second set up, where the ball will land somewhere on the inclined board and we will predict the distance which the ball traveled.

We are going to build a trajectory where the ball will land somewhere on the ground, where a carbon paper will be taped for us to know where it landed. By calculating the height of the table and the distance where it landed, we are going to find the ball's velocity when it is released from the trajectory. After this, we will attach an inclined board and estimate where the ball will land on the board.

These are the calculations our group did in order to find the ball's velocity when it is released from the trajectory, and the estimated distance where it will land on the board.

First, we built the trajectory in which the metal ball would travel. We calculated the height of the table to the ground, as well as the distance that the ball landed from the table on the carbon paper. We did this experiment about five times, to have a good estimate of the average distance. Using this information, we used kinematics to calculate the speed of the ball at the moment when it goes off the table. We then attached the inclined board to our equipment and calculated the degree which the board was inclined. From that, we used the equations: dcos(theta)=Vot and dsin(theta)=gt^2/2 to find the distance that the ball would land on the board.

Our experimental value gave us a distance of 0.28 meters on the board.

The theoretical value for d which we found was 0.317 meters on the board. Our theoretical value was .037 meters off. The relative difference was -11%. The uncertainty or error between the numbers could be human errors, natural errors, or air resistance acting on the ball during the period which it is in free fall.