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

2. 5/2 September–December 2009 University Physics: Mechanics Announcement 04.11.0918.30–20.30: Mid-term Examination (IE) 06.11.0918.30–20.30: Mid-term Examination (IT) Examination room will be informed on the exam day

3. 5/3 September–December 2009 University Physics: Mechanics 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

4. 5/4 September–December 2009 University Physics: Mechanics Solution of Homework 4: The Plane A 483 km, 45 min B C 966 km, 1.5 h Δr1Δr1 → (a) the magnitude of its displacement (b) the direction of its displacement Quadrant III Quadrant I Δr2Δr2 → AB C Δr total →

5. 5/5 September–December 2009 University Physics: Mechanics (c) the magnitude of its average velocity Solution of Homework 4: The Plane (d) the direction of its average velocity (e) its average speed Quadrant III

6. 5/6 September–December 2009 University Physics: Mechanics 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:

7. 5/7 September–December 2009 University Physics: Mechanics  We can rewrite the last equation as where the scalar components of are: Average Acceleration and Instantaneous Acceleration Acceleration of a particle does not have to point along the path of the particle

8. 5/8 September–December 2009 University Physics: Mechanics 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

9. 5/9 September–December 2009 University Physics: Mechanics 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.

10. 5/10 September–December 2009 University Physics: Mechanics 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.

11. 5/11 September–December 2009 University Physics: Mechanics Projectile Motion

12. 5/12 September–December 2009 University Physics: Mechanics Projectile Motion Two Golf Balls The vertical motions are quasi- identical The horizontal motions are different

13. 5/13 September–December 2009 University Physics: Mechanics Projectile Motion Analyzed The Horizontal Motion The Vertical Motion

14. 5/14 September–December 2009 University Physics: Mechanics Projectile Motion Analyzed The Horizontal Range Eliminating t, This equation is valid if the landing height is identical with the launch height v x = v 0x v y = –v 0y

15. 5/15 September–December 2009 University Physics: Mechanics Projectile Motion Analyzed Further examining the equation, If the launch height and the landing height are the same, then the maximum horizontal range is achieved if the launch angle is 45° Using the identity we obtain R is maximum when sin2θ 0 = 1 or θ 0 =45°

16. 5/16 September–December 2009 University Physics: Mechanics Projectile Motion Analyzed The launch height and the landing height differ The launch angle 45° does not yield the maximum horizontal distance

17. 5/17 September–December 2009 University Physics: Mechanics 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

18. 5/18 September–December 2009 University Physics: Mechanics Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. (a)Determine the maximum height h of the baseball above the ground h

19. 5/19 September–December 2009 University Physics: Mechanics Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. d (c)Determine the horizontal distance d it travels. (b)Determine the duration when the baseball is on the air.

20. 5/20 September–December 2009 University Physics: Mechanics released horizontally Example: Rescue Plane 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?

21. 5/21 September–December 2009 University Physics: Mechanics released horizontally Example: Rescue Plane 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

22. 5/22 September–December 2009 University Physics: Mechanics 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? Time for the stuntman to fall 4.8 m Horizontal distance jumped by the stuntman in 0.99 s He cannot make the jump