BKVP

Group Members: Alyssa Berger, Niki Kaiden, Bret Pontillo, Rory Vanderberg

__ Shoot Your Grade __
 * Introduction:** For this part of the project, we were given a launcher that had to be adjusted to medium speed, and we had to perform multiple tests and gather data on the ball's distance at different angles. As we experimented with different angles, we were told to gather enough information so that we could figure out the ball's initial velocity, maximum height, and range, and create excel graphs to witness our data. With all of this information, we were instructed to come up with an equation that allowed for us to simply plug in some numbers, and give us our desired results regarding the angle and distance of the launcher. On performance day, a 5 centimeter diameter hoop was hung from the ceiling, and using the equation we had come up with, we had to launch the ball so that it would make it through the center of the target. Each group had five tries in ten minutes.


 * **Theory/ Rationale:** We believe the results this experiment will produce will be that we will make every shot through the hoop. If our equations are correct and based on reliable data, then we should make all of the shots perfectly. **

For the calibration, our first material used was the launcher. This was the main portion of our lab in which the ball was launched from this instrument. We were allowed to use a meter stick to measure the range of the ball from the launcher, as well as to measure the y- value to see at what height the ball began at. Also, we were able to use a tape measure, which was easier to use than a meter stick when measuring the range of the ball from the carbon paper to the launching device. This was useful on the performance day as well, because we were able to place it along a path from the launcher to below the "hoop." The ball, clearly, was used as the object being launched. To get the ball into the launcher, we had a black cylinder that pushed the ball to the medium range position. We were also allowed to use physics textbooks to level out the ball's range. For instance, if the y-value was at 26 centimeters, than the physics textbooks would be stacked 26 cm high so you could plug your results into the "range" equation when the x-distance is equal. Carbon paper was used over regular paper so that we could observe where the ball landed, and with that, find the ball's range at a specific angle. Masking tape was allowed, not only used as a practice hoop, but also to hold down the carbon paper to either the floor, or the textbooks. Lastly, a calculator was allowed to verify your excel results and mathematically figure out the results for the ball's travel at a particular angle.
 * Materials for "Shoot Your Grade":**

For this part of the project, we first chose our launcher and immediately began experimenting with a variety of angles to see the range the ball traveled. The launcher was set on medium speed, and we used carbon paper to indicate the range of the ball's travel. For instance, when experimenting with a 40 degree angle, we would calibrate the launcher to 40 degrees, put carbon paper over regular paper a certain distance away, and when the ball would make a mark on the paper, we used a tape measure to find the distance the ball had traveled. We started with 0 degrees, and worked our way up to testing to 60 degrees. This process required a lot of time and work because not only did we have to line up the paper exactly where the ball would land, we also had to measure the distance the launched item traveled, as well as the height it started at. On excel, we recorded the ball's range, height, angle, and velocity with equations plugged in. With this information, we created graphs showing the maximum height versus the angle and graphs that showed the ball's range with a specific angle. This information gave us the x-value for the ball's range with a specific angle. This information would eventually help on the Performance Day. Then, an equation was created that would allow for us to plug in the height of the hoop on performance day, and we could receive the angle the ball should be at so that it would travel through the center of the hoop.
 * Procedure for "Shoot Your Grade" Calibration:**

We determined velocity through the equation. We were able to use this equation because we shot the launcher from the same height, as the height where the ball landed. To do that we had to stack up books to the same height of the launcher. To additionally see the equations which make up each column in the spread sheet click sheet one after downloading the following excel spreadsheet:
 * Graphs/ Data:**

On "Performance Day," we measured the distance from the center of the ring to the ground to find the max height. We then plugged the result into the excel spreadsheet. This gave us the range from the launcher to the ring and the angle the launcher should be inclined at. The result for a max height of the hoop was 145.2 meters above the launcher. So we set the launcher up 200m away at an angle of 55.5 degrees. We did not have many tests with the equation throughout the week but when we did test the equation we found out, it was off by 7-10 degrees. So when the projectile went through the hoop as seen below, we had to adjust the angle to 65 degrees.
 * Procedure For Shoot Your Grade Performance day:**

media type="file" key="LaunchDayBoom.m4v" width="300" height="300" This video depicts the final projectile launch that went through the center of the hoop and was a success!


 * Error Analysis:**



In conclusion, there were many errors that came along with this project that did not make our results as perfect as they could have been. When we performed our project, it hit the hoop once, went through the center once, and missed three times. The first error in figuring out the final equation so that the ball went through the center of the hoop on performance day was the root of our project, the launcher. Sometimes, on the same angle, the ball would travel completely different distances at medium speed. So, our results could never have been __**exact**__ if the launcher would sometimes give us a variety of results for a specific angle. Also, error could have been seen in the calculations of the velocity or maximum height. If those numbers did not appear to be accurate, then it would have been difficult to get an exact equation. Also, there was definitely some error in our equation that was used on performance day. Though it was not totally inaccurate, considering it hit the hoop and went through it once, our equation gave us the angle once we plugged in the height of the hoop and the range the launcher was at. It would have been **much** more beneficial to us if we had created an equation that would have provided us with the range as well as the angle with the provided maximum height, velocity, and acceleration. To address these errors in the future, we could have done more tests with each angle until we got an EXACT range so that our end results with the velocity would have been more exact. We also could have come up with an equation that would have provided the range the launcher needed to be, rather than us supplying a range and then developing the angle from there. On the actual performance day, the equation had told us to put the launcher at 55.2 degrees, though it ended up that the angle had to be at about 60 degrees. Though these numbers are not drastically different, it does have an affect on the results you hope to acquire.
 * Conclusion:**