1. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Physics I 95.141 LECTURE 5 9/20/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Outline Review of Lecture 4 Projectile Motion What do we know? –Units –Kinematic equations –Freely falling objects –Vectors –Kinematics + Vectors = Vector Kinematics –Relative motion

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Exam Prep Problem An object starts from rest at the origin. If the acceleration of the object is given by: A) (10pts) Give the velocity and displacement of the object, as a function of time. B) (5pts) What is the object’s velocity and speed at 10s? C) (5 pts) What is the object’s displacement at 10s? D) (5 pts) What is the average velocity of the object for the first 10 seconds of motion?

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Exam Prep Problem An object starts from rest at the origin. If the acceleration of the object is given by: A) (10pts) Give the velocity and displacement of the object, as a function of time.

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Exam Prep Problem An object starts from rest at the origin. If the acceleration of the object is given by: B) (5pts) What is the object’s velocity and speed at 10s?

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Exam Prep Problem An object starts from rest at the origin. If the acceleration of the object is given by: C) (5 pts) What is the object’s displacement at 10s?

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Exam Prep Problem An object starts from rest at the origin. If the acceleration of the object is given by: D) (5 pts) What is the average velocity of the object for the first 10 seconds of motion?

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion (displacement) Projectile motion is a special case of motion with constant acceleration: the acceleration due to gravity Here, the acceleration is in only one direction! The equations of motion become:

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion (Equations Of Motion)

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion (velocity) We can always find the expression for velocity by differentiating the expression for displacement with respect to time.

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion (acceleration) We can always find the expression for acceleration by differentiating the expression for velocity with respect to time.

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion Problem Solving Strategy –Draw a diagram, choose coordinate system –Split into x, y components of motion –Think about what problem is actually asking! –List unknowns and knowns –Apply relevant equations and solve

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Say I hit a golf ball with initial velocity v o at an angle of θº. –Find equations of motion –Find ball height as a function of lateral position (y(x)) –Find the Range of the ball (assuming ground is flat) –The time of flight

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem Say I hit a golf ball with initial velocity v o at an angle of θº. –A) Find equations of motion Draw diagram and choose coordinate system Fill in knowns Vxo Vyo x y

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem Say I hit a golf ball with initial velocity v o at an angle of θº. –B) Find y(x) Write out equations Solve for y(x)

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem Say I hit a golf ball with initial velocity v o at an angle of θº. –C) Find Range (distance ball travels before hitting ground) What does this mean in numbers? x y

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem (Extra) Say I hit a golf ball with initial velocity v o at an angle of θº. –C+) Find the θ for maximum Range What does this mean in numbers? x y

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem Say I hit a golf ball with initial velocity v o at an angle of θº. –D) Find time of flight (time ball travels before hitting ground) What does this mean in numbers? x y

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Projectile Motion For a typical projectile motion problem, we can think about the object motion in component form.

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem A punter, on average, can give the football an initial velocity of 27m/s. The Cowboy’s new $1.2 Billion stadium has a scoreboard 90ft (27.5m) off the ground. What is the minimum angle required for an average punt to hit the scoreboard? –Find initial y-velocity required to hit scoreboard

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example Problem A punter, on average, can give the football an initial velocity of 30m/s. The Cowboy’s new $1.2 Billion stadium has a scoreboard 90ft (27.5m) off the ground. What is the minimum angle required for an average punt to hit the scoreboard? –What is angle?

22. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 The Speed Bus OK, so we know: 1)DRAW DIAGRAM!! 2)Determine knowns 3)Pick Equations

23. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Speed Bus with Magic Launch OK, so we know new 1)DRAW DIAGRAM!! 2)Determine knowns 3)Pick Equations

24. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Does it make it?

25. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example (Rescue Helicopter) Helicopter wants to drop supplies on mountain top 200m below. Helicopter flying horizontally at 70m/s –A) How far in advance (horizontal distance) should the package be dropped? Draw diagram, choose coordinate system Knowns and unknowns

26. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Helicopter, Part (a) Divide equations into x and y

27. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Example (Rescue Helicopter) Helicopter wants to drop supplies on mountain top 200m below, 400m in advance. Helicopter flying horizontally at 70m/s –B) What vertical velocity should the package be given? Draw diagram, choose coordinate system, time interval Write out equations

28. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Helicopter, Part (b) Divide equations into x and y

29. Department of Physics and Applied Physics 95.141, F2010, Lecture 5 Now We Know Projectile Motion –Motion in component form –Problem solving approach