Lab #4 Informal Report - Projectile Motion

Sierra Altman, Jurnee Ingram & Cammy Davenport Informal Lab Report #4 Physics 101-03 Dr. Mahmud Sefannaser 11 January 2024 Lab #4 Report - Projectile Motion Introduction: The purpose of this lab was to speculate the locality of the projectile’s landings using measurements and the kinematic equations. The data was collected using the equipment (projectile launcher with a ball, carbon paper, grid paper, c-clamps, and measuring tape) to determine the initial velocity and the time of flight of the projectile to then find the distance of all landings to establish the standard deviation from the data set. The launch angle was set to 0 degrees to calculate the displacement of the projectile for ten trails, data was collected and a standard deviation was set. The launcher was changed to an angle of 30 degrees and a projectile was shot for ten trials. From the data we gathered, we used it to calculate the distance, time, and velocity. We then compared the results at the end to how close the ball would be to our prior predictions. We concluded that the predictions were slightly off due to human error. The main principle of this experiment was to break down projectile motion into two independent motions, X axis motion (horizontal) and Y axis motion (vertical). We need to understand velocity and displacement to determine how other variables like gravity can affect them. Velocity is the movement of an object from it’s initial position through speed, direction, and displacement. Procedure For this procedure, the team used a projectile launcher to determine the velocity and time of flight of the projectile. We first clamped the launcher to the table, this stayed constant throughout the experiment. The launch angle was set at 0 degrees so we could calculate the distance of the projectile launched at 0 degrees. Then, the grid paper was placed on the table with the carbon paper on top above where the first test shot landed. We continued this experiment 10x. After this, we calculated the velocity and time of flight. Next, the average distance of all projectile landings and the standard deviation was calculated. In the second part of the experiment, the displacement of the projectile is launched at 30 degrees from the launcher for another 10x. We found the average distance of all projectiles shot and calculated the standard deviation for the set data. Finally, to see if the information was correct, the team placed paper at the predicted displacement (from the data calculated) and launched the same projectile from the launcher at the same height at the same launch angle of 30 degrees. After launching, we observed where the ball landed in proximity to where we predicted. Results

Data collected in the initial ten launches of the projectile at 0 degrees is shown in table 1. There are ten trials, and the distance in the x direction that the projectile traveled for each trial is shown in the “Horizontal Distance” column, measured in meters. The average distance of all of the trials and the standard deviation, is shown below. The time elapsed is then calculated using the initial height and the knowledge that the initial velocity in the y direction of a horizontally launched object is zero and gravity (9.8 m/s 2 ). Using the equation, Δy=v 0y t+½-gt 2 , with Δy being the initial height of 0.6813 m, v 0y being zero and g being 9.8 m/ s 2 , the time elapsed in seconds is calculated. Using the average distance traveled in the x direction and time found, the initial velocity is calculated and this can be used to calculate the initial velocity in both the x and y directions when the projectile is launched at the angle of 0 degrees. The initial velocity is used in the Δy=v 0y t+½-gt 2 to find the time and with the time, the initial velocity calculated. The Δx=vt equation is used to find Δx. The projectile is then launched at an angle of 0 degrees to test the answer for Δx found. At 0 degrees, the average horizontal distance ( Δx) is 0.6813 m and the initial velocity is 27.1 m/s 2 and now with the angle set at 30 degree angle, the vertical distance is Δy is 30 cm and the initial velocity is 40.2 m/s, and the calculated time to be 3.43 sec. Finally, the predicted horizontal distance is 92.95m and when the final launch was launched to test the Δx, there was a 5.53% error found. 2 Data: Vertical distance: 30 cm Angle Above Horizontal: 30 degrees Initial velocity: 40.2 m/s 2 Calculated time of Flight: 3.43 sec Predicted horizontal distance: 92.95 cm Trial # Horizontal Distance (M) 1 67.4 cm 2 67.6 cm 3 67.8 cm 4 67.6 cm 5 68.2 cm 6 68.5 cm 7 69.0 cm 8 68.6 cm