Project

Lab Instructions V0.0 January 29, 2018

Projectile Motion

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1 Objective

To experimentally study projectile motion.

2 Overview

Recall that a projectile is an object that is in free-fall, i.e., it moves while being subjected to just the Earth’s gravity. When a projectile remains close to the surface of the earth and it’s trajectory spans a distance much less than the earth’s circumference, its horizontal and ver- tical motion get decoupled. It’s horizontal motion (say, x-direction) proceeds with constant velocity, while it’s vertical motion (say, y-direction) proceeds as motion with constant ac- celeration ~a = (g, pointing vertically down), where g = 9.8m/s2. The projectile’s trajectory, x vs.y curve, can then be readily derived from it’s x vs.t and y vs.t equations, by eliminating t. In this experiment, you will have a shooter that can launch a projectile at one of three possible, but unknown, speeds, and a continuously adjustable angle, which you can read-off from the built-in protractor.

The main idea of this experiment is to launch a projectile, first, to determine its unknown speed, by measuring the (x,y) coordinates at which the projectile lands, given it’s angle of launch θ. Next, choose a different target, and predict the angle of launch θ that would land the projectile at the chosen target. Finally, experimentally, verify your prediction by checking if the projectile indeed hits the target.

3 Apparatus

Simulation: https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile- motion_en.html

For use by the physics department, Ohlone College, Fremont, CA.

Lab Instructions V0.0 January 29, 2018

5 Overall experimental set up

Figure 1: Experimental Setup

For use by the physics department, Ohlone College, Fremont, CA.

Figure 2: Coordinate System and Trajectory

Lab Instructions V0.0 January 29, 2018

1. Choose your coordinate system: axis and origin. The cross-hair marks the exact position of the launch

2. Carefully measure the initial vertical position y0 and horizontal position x0 of the cross-hair. measure distances relative to x0,. Record (x0, y0) with the experimental data.

6 Part 1: Determine the initial launch speed v0 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 θ = {15◦, 45◦, 75◦}

2. For each launch angle θi, i = 1, ...,N, launch the projectile for M = 3 to 5 times. For each shot, record the (xj,yj),j = 1, ...,M coordinates of the impact point.

3. Compute the average coordinates, (< xi >,< yi >), for each θi.

For use by the physics department, Ohlone College, Fremont, CA.

4. Recall that the equation for the trajectory of the projectile is given by:

y = y0 + tan θi(x−x0) − 1

2 g

(x−x0)2

v0i2 cos2 θi (1)

Derive the above equation in a separate section in your lab report.

5. Using x0, y0, θi, x =< xi > and y =< yi >, calculate the initial launch speed, v0i, from the equation of the trajectory above. Thus, you will have a single launch speed for each θi.

Note: Assume the you don't know the speed even though you can see that in simulation

Lab Instructions V0.0 January 29, 2018

Table 1: Data for Part 1

x0 =?,y0 =?, θi xj yj < xi > < yi > v0i θ1 =? M data points M data points single value single value single value

θ2 =? M data points M data points single value single value single value

... ... ... ... ... ...

θN =? 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 = y0, maximum range is achieved at θ = 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.

2. Position the target .The idea is to choose yT , the y− coordinate of the target to be different from the y coordinate in Part 1 (Check Appendix).

3. You might have to redefine your axis and origin. Carefully measure the coordinates (xT , yT ) of the target, and if needed, y0 and x0 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 θ. Hint: try to re-write the equation in terms of a single trigonometric function, instead of two trigonometric functions.

6. The predicted angle and shoot!

For use by the physics department, Ohlone College, Fremont, CA.

Table 2: Data for Part 2 x0 y0 xT yT θpred Did θpred work?

Lab Instructions V0.0 January 29, 2018

8 Conclusion

Briefly summarize your findings.

For use by the physics department, Ohlone College, Fremont, CA.

Appendix