Figure 2: Coordinate System and Trajectory 4. Choose your coordinate system: axis and origin. One choice for the origin is on the table, vertically below the cross-hair on the PL. The cross-hair marks the exact position of the launch, i.c., when the spring inside the PL disengages with the ball, and the ball's projectile motion begins. 5. Carefully measure the initial vertical position yo and horizontal position zo of the cross-hair. Mark the r-coordinate with a piece of masking tape and pencil mark. This way you can conveniently measure distances relative to me,. Record (To, Mo) with the experimental data. 6. First experiment with launching, and determine the general area in which the ball lands, for say, 8 = 0" and 0 = 45". 7. Make sure that you are able to launch gently enough, so that the PL does not move. 8. Then, take a shoot of carbon paper, carbon-side up and place a white shoot of paper on top of it. Tape them together onto the table, so that the projectile's impact will leave an imprint on the paper. 6 Part 1: Determine the initial launch speed vn for a set of launch angles. 6.1 Experimental data and calculations 1. Follow the steps below, to determine the launch speed for N = 3 different launch angles 0 = (150, 45%, 759} 2. For cach launch angle 6, i = 1, ..., N, launch the projectile for M = 3 to 5 times. For each shot, record the (x,, y,), j = 1, ..., M coordinates of the impact point. 3. Compute the average coordinates, (, ), for cach &.4. Recall that the equation for the trajectory of the projectile is given by: # = Do | Land,(1 - To) (1) Derive the above equation in a separate section in your lab report. 5. Using So, 10, 6, I = and y =, calculate the initial launch speed, up, from the equation of the trajectory above. Thus, you will have a single launch speed for each da- Table 1: Data for Part 1 In =Y, VO =?, 0. M data points M data points single value single value single value M data points M data points| single value single value single value M data points M data points single value single value single value 6.2 Analysis and discussion 1. Does the launch speed depend significantly upon the launching angle? Is it reasonable? 2. Show that for y = The maximum range is achieved at 0 = 45. Approximately, for what angle do you achieve maximum range? Do you expect it to be different from 45'? If so, why? 7 Part 2: Predict the launch angle required to hit a chosen target 7.1 Experimental data and calculations 1. Choose a target that is different from Part 1. For example, you can choose a small cup or bowl or trace a small circle on a sheet of paper. 2. Position the target on the floor or raised on top of a stack of books. The idea is to choose yy, the y-coordinate of the target to be different from the y coordinate of the carbon-baber in Part 1. You can even choose the target to be a circle drawn on the3. You might have to redefine your axis and origin. Carefully measure the coordinates (ry, By) of the target, and if needed, yo and In again. 4. FIRST CALCULATE (See next step). Shoot only AFTER you calculate, and only at the predicted angle. 5. Predict the correct launch angle: Solve the equation of the trajectory for the unknown 8. Hint: try to re-write the equation in terms of a single trigonometric function, instead of two trigonometric functions. 6. Orient the PL to launch at the predicted angle and shoot! 7. Show the instructor your calculation of the predicted angle and demo the shot. Table 2: Data for Part 2 IT Bored Did Opred work? 8 Conclusion Briefly summarize your findings.15 Degree Angle H = 105 cm = 1.05 m 1. 285 cm = 2.85 m 2. 285 cm = 2.85 m 3. 286 cm = 2.86 m 4. 286 cm = 2.86 m 5. 286 cm = 2.86 m V = 12.107 m/s 45 Degree Angle H = 106 cm = 1.06 m 1. 117 cm = 1.17 m 2. 304 cm = 3.04 m 3. 306 cm = 3.06 m 4. 305 cm = 3.05 m 5. 305 cm = 3.05 m V = 6.76 m/s 75 Degree Angle H = 105 cm = 1.05 m 1. 85 cm = 0.85 m 2. 85.25 cm = 0.8525 m 3. 88 cm = 0.88 m V =4.99 m/s