2-d Kinematics Simulation-
1. Go to https://phet.colorado.edu/en/simulation/projectile-motion
2. Download the program or select "run now", depending on your preferences.
3. Play around with the simulation until you get comfortable. You can also move around a target to see if you can hit it by estimating. Note that there is a tape measure. There are six parameters you can vary:
o angle
o initial height (click and drag up or down on the cannon)
o initial speed
o mass
o diameter
o air resistance drag coefficient (don't vary the altitude yet).
4. In the absence of air resistance, which of the five (5) other parameters affect the range? How do they do so (does an increase in the parameter increase the range, decrease the range, or is it more complicated)? Note that there are five (5) parameters you can manipulate. Manipulate them all. Once you think you are done, count the number of parameters you manipulated and make sure that the number is five (5).
5. In the presence of air resistance with a constant drag coefficient, which of the five (5) other parameters affect the range? How do they do so (does an increase in the parameter increase the range, decrease the range, or is it more complicated)? Once you think you are done, count the number of parameters you manipulated and make sure that the number is five (5).
6. Perform a test with air resistance on, then repeat the test with air resistance off . Sometimes you will get a similar range (air resistance is negligible) while other times you will get a very different range (air resistance is significant). Try this under a wide variety of conditions in order to make generalizations about air resistance. Then complete the following sentence: air resistance is negligible when ...
7. Remove the air resistance. Place the cannon and the target 24 meters apart at the same height (note that this will require raising the target above the ground a bit). Use a kinematics equation from the text or tip sheet to find an angle and initial speed that will hit the target. Note that multiple solutions are possible. Show your work below. Did your prediction work?
8. Keep the air resistance off. Raise the cannon significantly above the ground. Find (through guess and check, not kinematics) and record the angle of maximum launch distance for a fixed velocity (don't pick a large velocity). Is this what you expected?
9. Add the air resistance and select baseball. The world record baseball throw on level ground was reported as 445 feet and 10 inches at an altitude of 1040 feet (this is not the initial or maximum height of the throw; it merely affects the air resistance). What was the minimum speed (in both m/s and mph) and optimal angle of this throw according to the simulation? You will simply need to use guess and check as the constant acceleration kinematics equations do not apply to this situation with significant air resistance. Note that will need to estimate a plausible initial height for the release. Note also that the simulation can't take into account tailwind and ball spin, so your estimate of launch speed will be off.