1. Lecture 5: Kinematics in 2-3D Physics 218 Alexei Safonov

2. Checklist for Today • For the rest of this week: • Be ready for the lab (WebAssign) including pre-labs • Quiz at the recitation on Chapter 2 • There was a pre-lecture for today • Many people completed, but not all • A pre-lecture due Wednesday morning • Don’t forget the checkpoints • Homework for Chapter 3 is due Sunday on MP • Coming week recitation quiz will be on Chapter 3

3. Throw a Ball up You throw a ball upward into the air with initial velocity V0. Calculate: • The time it takes to reach its highest point (the top). • Distance from your hand to the top • Time to go from your hand and come back to your hand • Velocity when it reaches your hand • Time from leaving your hand to reach some random height h.

4. Speeder A speeder passes you (a police officer) sitting by the side of the road and maintains their constant velocity V. You immediately start to move after the speeder from rest with constant acceleration a. • How much time does it take to ram the speeder? • How far do you have to travel to catch the speeder? • What is your final speed? X Police Officer Speeder

5. Chapter 3 • Kinematics in Two or Three Dimensions • Projectile Motion • Uniform Circular Motion

6. Important Equations of Motion If the acceleration is constant Position, velocity and Acceleration are vectors.

7. z ^ k y x ^ ^ j i Position in 3 dimensions

8. z ^ k y x ^ ^ j i Velocity in 3 dimensions

9. Projectile Motion The horizontal and vertical equations of the motion behave independently Problem solving: The trick for all these problems is to break them up into the X and Y directions.

10. Constant Acceleration

11. Kinematics in 3D

12. Checkpoint 1 A physics demo launches one marble horizontally while at the same instant dropping a second marble straight down. Which one hits the ground first? A)The launched marble hits first. B)The dropped marble hits first. C)They both hit at the same time. DEMO

13. Ball Dropping • Analyze Vertical and Horizontal separately!!! • Ay = g (downwards) • Ax = 0 • Constant for Both cases!!! Vx = 0 Vx>0

14. Projectile Motion The horizontal and vertical equations of the motion behave independently Problem solving: The trick for all these problems is to break them up into the X and Y directions.

15. Projectile Motion & Frames of Reference

16. Projectile Motion Vertical Horizontal Boring

17. Monkey Troubles You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?

18. Shooting the Monkey… Dart x= vot Monkey x = xo

19. Shooting the Monkey… Dart hits themonkey Still works even if you shoot upwards! y = yo-1/2 g t2 y = voy t -1/2 g t2

20. Marbles & Math • Prove mathematically that an object projected horizontally will reach the ground at the same time as an object dropped vertically

21. Firing up in the air at an angle A ball is fired up in the air with velocity Vo and angle Qo. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here?

22. h Football Punt • A football is kicked at angle Q0 with a velocity V0. The ball leaves the punters foot h meters above the ground. • The velocity at the maximum height • How far does it travel, in the X direction, before it hits the ground? • What angle maximizes the distance traveled

23. Checklist for Today • For the rest of this week: • Be ready for the lab (WebAssign) including pre-labs • Quiz at the recitation on Chapter 3 • There was a pre-lecture for today • Many people completed, but not all • A pre-lecture due Wednesday morning • Don’t forget the checkpoints • Homework for Chapter 3 is due Sunday on MP • Coming week recitation quiz will be on Chapter 3