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

2. 5/2 Erwin SitompulUniversity 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

3. 5/3 Erwin SitompulUniversity 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 →

4. 5/4 Erwin SitompulUniversity 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

5. 5/5 Erwin SitompulUniversity Physics: Mechanics  When a particle’s velocity changes from v 1 to v 2 in a time interval Δt, its average acceleration a avg during Δt is:  If we shrink Δt to zero, then a avg approaches the instantaneous acceleration a ; that is: Average and Instantaneous Acceleration →→ → → →

6. 5/6 Erwin SitompulUniversity Physics: Mechanics  We can rewrite the last equation as where the scalar components of a are: Acceleration of a particle does not have to point along the path of the particle Average and Instantaneous Acceleration →

7. 5/7 Erwin SitompulUniversity Physics: Mechanics A particle with velocity v 0 = –2i + 4j m/s at t = 0 undergoes a constant acceleration a of magnitude a = 3 m/s 2 at an angle 130° from the positive direction of the x axis. What is the particle’s velocity v at t = 5 s? Solution: Thus, the particle’s velocity at t = 5 s is Average and Instantaneous Acceleration ^ → → ^ → At t = 5 s,

8. 5/8 Erwin SitompulUniversity Physics: Mechanics Projectile Motion  Projectile motion: a motion in a vertical plane, where the acceleration is always the free-fall acceleration g, which is downward.  Many sports involve the projectile motion of a ball.  Besides sports, many acts also involve the projectile motion. →

9. 5/9 Erwin SitompulUniversity 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.

10. 5/10 Erwin SitompulUniversity Physics: Mechanics Projectile Motion

11. 5/11 Erwin SitompulUniversity Physics: Mechanics Projectile Motion Two Golf Balls The vertical motions are quasi- identical. The horizontal motions are different.

12. 5/12 Erwin SitompulUniversity Physics: Mechanics Projectile Motion Analyzed The Horizontal Motion The Vertical Motion

13. 5/13 Erwin SitompulUniversity Physics: Mechanics 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 Projectile Motion Analyzed

14. 5/14 Erwin SitompulUniversity Physics: Mechanics 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°. Projectile Motion Analyzed

15. 5/15 Erwin SitompulUniversity Physics: Mechanics Projectile Motion Analyzed The launch height and the landing height differ. The launch angle 45° does not yield the maximum horizontal distance.

16. 5/16 Erwin SitompulUniversity 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 this chapter is based on this assumption

17. 5/17 Erwin SitompulUniversity Physics: Mechanics 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 Example: Baseball Pitcher

18. 5/18 Erwin SitompulUniversity Physics: Mechanics 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. Example: Baseball Pitcher

19. 5/19 Erwin SitompulUniversity Physics: Mechanics 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 Φ of the pilot’s line of sight to the victim when the capsule release is made? Example: Rescue Plane

20. 5/20 Erwin SitompulUniversity Physics: Mechanics (b)As the capsule reaches the water, what is its velocity v in unit-vector notation and in magnitude-angle notation? → 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. Unit-vector notation Magnitude-angle notation Example: Rescue Plane

21. 5/21 Erwin SitompulUniversity Physics: Mechanics 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 Example: Clever Stuntman