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In many sport activities the performer moves freely through the air. Diving, gymnastics, high jumping, long jumping and figure skating are a few examples where such motion occurs. In addition, sports implements are projected in events like the shot-put, discus, baseball and soccer. In both situations, the motion is that of a "projectile" and is controlled by well understood physical laws.
Once the projectile (either performer or projected object) is in the air, only two external forces act upon it. The first is the force of gravity acting vertically and the second is due to air drag effects acting in a direction primarily opposite to the direction of motion. The latter force is an important factor in such sports as ski-jumping and skydiving because the velocity is quite high and the flight time is quite long. It is also of special significance in the javelin and discus events because of the aerodynamic characteristics of the implements involved. However, in many activities involving projectile motion air resistance plays an insignificant role. Because of this and in order to simplify the following calculations, we will neglect the air resistance forces that are involved. We will assume such forces to be zero.
This lab will consist of three sections dealing with projectile motion. The first section will consider motion from ground level in a soccer kick. Velocity components of the ball will be determined from video images. In the second section, motion of a projectile beginning above ground level (shotput) will be determined. The final section will use results from these previous measurements to determine the trajectory of the projectiles in each case.
Part 1: Projectile motion beginning from ground level is the simplest to analyze. The ultimate motion depends only on the velocity components of the object at the point of takeoff. This part of the lab will determine the horizontal and vertical velocity components of a soccer ball as it was kicked from ground level.
Five video images have been saved for the analysis. Using similar methods to the analysis last week, first determine the ball position (center) in each picture using the computer image coordinates. Convert these to normal rectangular coordinates scaled to real life size. Use the 1 meter scale of the last figure to determine an appropriate conversion factor.
NOTE: This technique for finding coordinates works on the web browser installed on the lab computers and on some but not all other web browsers. If on your browser the coordinates do not show up in the status bar at the bottom of the page, click on the image. The page will be reloaded and the coordinates will show up at the end of the location bar (with the URL or address).
Determine the velocity components through each interval but particularly note the components from frame 3 to 4 immediately after the ball was kicked. The sequence of pictures was recorded at 30 frames per second. Hence the time interval between pictures was 0.033 seconds.
Measure and analyze the following pictures:
Part 2: The motion of a shot-put is determined at release by its velocity (speed and angle) and by its height of release. Use the flight time equation which was derived in the lab introductory lecture to calculate the distance of a set of tosses at varying release angles to determine the optimum angle for maximum distance. Assume a constant speed at release of 15 m/s and a constant release height of 2 meters. Use a spreadsheet to do these calculations; format your sheet in a manner similar to this example table.
From your spreadsheet, determine what the optimal angle of release is for a shotput which was released with the given conditions.
Part 3: Based on your results in Parts 1 and 2, create two spreadsheets which determine the TRAJECTORY of the soccer ball and the shotput throughout each flight. Given the initial conditions in each case, write formulas for the horizontal and vertical positions as a function of time. Apply these formulas for the range of times from release to impact. Then use these position data to plot trajectory (Y vs X, not Y vs time).
Based on the results you have obtained, write a brief essay which discusses the relationship of Height and Angle of Release to performance for a shotput. Include responses to the following questions in your discussion. Answering these questions may require returning to your spreadsheets and trying additional heights and velocities. Attach printouts of your graphs and spreadsheets to the written paper and return these to your lab instructor at the beginning of the next lab meeting.
