Projectile Motion

1. Projectile Motion AP Physics: Mechanics 2D Motion

2. Monkey and the Hunter Can a monkey be hit with a tranquilizer dart from far away if the monkey drops from a branch at the same time as the dart is shot?

3. Two Assumptions • The rate of gravitational acceleration is constant • Air resistance is negligible • What shape trajectory do we expect?

4. Hang-Time Question: How can the “hang-time” or “time of flight” of a horizontally fired projectile be extended? What factors affect the flight time of a projectile? Challenge: • Design and carry out a quick experiment using a tennis ball, a stopwatch, and a tape measure that will answer the questions above.  • Put the data that you collect on a whiteboard and convince the class that you are correct by the end of the period. • Turn in one sheet per group that has your data and explanations.

5. Hang-time DOES NOT depend upon initial horizontal velocity No forces in the x direction, therefore no change in velocity in the x direction. The ball stops due to gravity, so only a higher launch point will increase the hang-time of a horizontally fired projectile.

6. Hang-Time v0x ay=g y x

7. Horizontal Range • Question: What determines the distance that a horizontally fired projectile will travel? • Challenge: • Predict the Range of a horizontally fired projectile. Check your prediction and calculate your percent error. • Carry out this experiment using a steel ball and the provided trajectory apparatus. • For this experiment you should turn in the work that shows your prediction. Explain the reasoning behind your prediction. Show why you believe that you had a high or low percent error. • You should also include a general equation for the range of a horizontally fired projectile.

8. Horizontal Range v0x d ay=g h R

9. Rocket Science • Question: How does angle affect the time of flight and the range of a projectile? • Challenge: 1) Answer the question above. Provide evidence (data tables and graphs) to support your findings. Consider and report sources of error and ways to improve the lab. 2) Make predictions about which angle will make the greatest and least range. Find the initial velocity of the rocket and predict its range. Compare this to the actual range. 3) Make predictions about which angle will make the rocket spend the most time in the air. Compare your calculated hang-times to actual values from a stopwatch. 4) Turn one response in per group.

10. Rocket Science • Safety: The rockets are potentially VERY dangerous. The rockets leave the launcher at speeds exceeding 60 mph. If you do not give complete attention to the lab, you or someone else could be seriously injured. • NEVER look directly down at the rocket while it is on the launcher. • ALWAYS disconnect the air supply before touching a rocket which is on the launcher. • NEVER make any attempts whatsoever that even remotely look to me like you are going to launch the rocket at another individual. • NEVER attempt to catch a rocket while in flight. • NEVER launch the cap by itself. • Note: Since this lab is being done on the football field, we will measure everything in yards instead of meters. Make sure to convert your value of acceleration due to gravity (g).

11. (R/2,h) & (R,0) What are R horizontal range and h maximum height in terms of v0, g, and θ0?

12. substitute ttop

13. (R/2,h) & (R,0) What are R horizontal range and h maximum height in terms of v0, g, and θ0?

14. Substitute 2ttop

15. How can we express maximum range? When is this expression a maximum?

19. Kinematic Equations in 2D

20. The shape of a projectile’s trajectory Substitute

21. The shape of a projectile’s trajectory Quadratic!!! Parabola!!!

22. Conclusions Projectile motion is a superposition of two motions. 1) Constant velocity motion in the initial direction. 2) The motion of a particle freely falling in the vertical direction under constant acceleration.