University Physics: Mechanics

1. University Physics: Mechanics Ch4. TWO- AND THREE-DIMENSIONAL MOTION Lecture 5 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com

2. Announcement 04.11.09 18.30–20.30 : Mid-term Examination (IE) 06.11.09 18.30–20.30 : Mid-term Examination (IT) Examination room will be informed on the exam day University Physics: Mechanics

3. Homework 4: The Plane A plane flies 483 km west from city A to city B in 45 min and then 966 km south from city B to city C in 1.5 h. From the total trip of the plane, determine (a) the magnitude of its displacement (b) the direction of its displacement (c) the magnitude of its average velocity (d) the direction of its average velocity (e) its average speed University Physics: Mechanics

4. → → Δr1 Δr2 B A C → Δrtotal Solution of Homework 4: The Plane B A 483 km, 45 min 966 km, 1.5 h (a) the magnitude of its displacement (b) the direction of its displacement C • Quadrant I • Quadrant III University Physics: Mechanics

5. Solution of Homework 4: The Plane (c) the magnitude of its average velocity (d) the direction of its average velocity • Quadrant III (e) its average speed University Physics: Mechanics

6. Average Acceleration and Instantaneous Acceleration • When a particle’s velocity changes from to in a time interval , its average acceleration during is • If we shrink to zero, then approaches the instantaneous acceleration ; that is: University Physics: Mechanics

7. Average Acceleration and Instantaneous Acceleration • We can rewrite the last equation as where the scalar components of are: Acceleration of a particle does not have to point along the path of the particle University Physics: Mechanics

8. Average Acceleration and Instantaneous Acceleration A particle with velocity at undergoes a constant acceleration of magnitude at an angle from the positive direction of the x axis. What is the particle’s velocity at ? Solution: Thus, the particle’s velocity at is University Physics: Mechanics

9. Projectile Motion • Projectile motion: a motion in a vertical plane, where the acceleration is always the free-fall acceleration , which is downward. • Many sports involve the projectile motion of a ball. • Besides sports, many acts also involve the projectile motion. University Physics: Mechanics

10. Projectile Motion • Projectile motion consists of horizontal motion and vertical motion, which are independent to each other. • The horizontal motion has no acceleration (it has a constant velocity). • The vertical motion is a free fall motion with constant acceleration due to gravitational force. University Physics: Mechanics

11. Projectile Motion University Physics: Mechanics

12. Projectile Motion Two Golf Balls • The vertical motions are quasi-identical • The horizontal motions are different University Physics: Mechanics

13. Projectile Motion Analyzed The Horizontal Motion The Vertical Motion University Physics: Mechanics

14. Projectile Motion Analyzed The Horizontal Range Eliminating t, vx= v0x vy= –v0y • This equation is valid if the landing height is identical with the launch height University Physics: Mechanics

15. Projectile Motion Analyzed Further examining the equation, Using the identity we obtain R is maximum when sin2θ0 = 1 or θ0 =45° • If the launch height and the landing height are the same, then the maximum horizontal range is achieved if the launch angle is 45° University Physics: Mechanics

16. Projectile Motion Analyzed • The launch height and the landing height differ • The launch angle 45° does not yield the maximum horizontal distance University Physics: Mechanics

17. Projectile Motion Analyzed The Effects of the Air • Path I: Projectile movement if the air resistance is taken into account • Path II: Projectile movement if the air resistance is neglected (as in a vacuum)Our calculation along the chapter is based on this assumption University Physics: Mechanics

18. Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. h (a) Determine the maximum height h of the baseball above the ground University Physics: Mechanics

19. Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. d (b) Determine the duration when the baseball is on the air. (c) Determine the horizontal distance d it travels. University Physics: Mechanics

20. Example: Rescue Plane released horizontally A rescue plane flies at 198 km/h and constant height h = 500 m toward a point directly over a victim, where a rescue capsule is to land. (a) What should be the angle of the pilot’s line of sight to the victim when the capsule release is made? University Physics: Mechanics

21. Example: Rescue Plane released horizontally A rescue plane flies at 198 km/h and constant height h = 500 m toward a point directly over a victim, where a rescue capsule is to land. (b) As the capsule reaches the water, what is its velocity in unit-vector notation and in magnitude-angle notation? unit-vector notation magnitude-angle notation University Physics: Mechanics

22. Example: Stuntman A stuntman plans a spectacular jump from a higher building to a lower one, as can be observed in the next figure. Can he make the jump and safely reach the lower building? He cannot make the jump Time for the stuntman to fall 4.8 m Horizontal distance jumped by the stuntman in 0.99 s University Physics: Mechanics