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University Physics: Mechanics

University Physics: Mechanics. Ch 4 . TWO- AND THREE-DIMENSIONAL MOTION. Lecture 5. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. 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.

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University Physics: Mechanics

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

  2. 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. → → Δr2 Δr1 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

  4. 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

  5. Average and Instantaneous Acceleration → → • When a particle’s velocity changes from v1 to v2 in a time interval Δt, its average acceleration aavg during Δt is: → → • If we shrink Δt to zero, then aavg approaches the instantaneous acceleration a ; that is: →

  6. Average and Instantaneous Acceleration • We can rewrite the last equation as → where the scalar components of aare: Acceleration of a particle does not have to point along the path of the particle

  7. Average and Instantaneous Acceleration ^ ^ → A particle with velocity v0 = –2i + 4j m/s at t = 0 undergoes a constant acceleration a of magnitude a = 3 m/s2 at an angle 130° from the positive direction of the x axis. What is the particle’s velocity v at t = 5 s? → → Solution: At t = 5 s, Thus, the particle’s velocity at t = 5 s is

  8. 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. 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. Projectile Motion

  11. Projectile Motion Two Golf Balls • The vertical motions are quasi-identical. • The horizontal motions are different.

  12. Projectile Motion Analyzed The Horizontal Motion The Vertical Motion

  13. 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.

  14. 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°.

  15. Projectile Motion Analyzed • The launch height and the landing height differ. • The launch angle 45° does not yield the maximum horizontal distance.

  16. 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. 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.

  18. 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.

  19. 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 Φ of the pilot’s line of sight to the victim when the capsule release is made?

  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. (b) As the capsule reaches the water, what is its velocity v in unit-vector notation and in magnitude-angle notation? → Unit-vector notation Magnitude-angle notation

  21. Example: Clever 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

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