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10/3

10/3. Tests are not graded. If you were absent yesterday you can take the test today after school Solve now: A stone is dropped from a window 33.1m above the ground. How long does it take the stone to land? With what speed did it hit the ground? 2.60 s 25.5 m/s. 10/8 Pick up lab sheet.

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10/3

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  1. 10/3 • Tests are not graded. If you were absent yesterday you can take the test today after school • Solve now: A stone is dropped from a window 33.1m above the ground. How long does it take the stone to land? With what speed did it hit the ground? • 2.60 s 25.5 m/s

  2. 10/8 Pick up lab sheet • Tests are available for viewing before or after school. • Today we are doing a ball toss lab outside. This will be due at BOC tomorrow. • Thursday we will discuss special situations with PM-you will then be able to complete the rest of PM I • Friday is Q & A • Tuesday is the PM test (PM I WS due)

  3. Ball Toss Lab • Measure distance between the two people in feet • Each person will throw the ball 3x. Record and average your toss time. The 2nd person will then repeat this. You will need a third person to time. • Everyone must have their own times! • If you know the total time and distance, what else can you figure out? • This is due at the beginning of class tomorrow. Show all work on back. Answer the questions on the bottom. In table, for unknowns, enter formula used rearranged to solve for variable if needed.

  4. 10/9 • Turn in lab to sorter • Report cards will be handed out tomorrow • Today will discuss special situations with PM-you will then be able to complete the rest of PM I • Friday is Q & A • Tuesday is the PM test (PM I WS due)

  5. Projectile Motion Thank you Physics Classroom: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/usage.html

  6. What forces are working on the arrow as it flies horizontally through the air? 15 mph

  7. FORCE • A Push or Pull • If velocity constant, the force of thrust is equal but opposite the force of air friction • Is the arrow falling? The downward force working on the arrow is GRAVITY. This is greater than the upward force of air resistance. • Anything thrown or launched on this planet is under the influence of gravity.

  8. What keeps the arrow moving forward? • Inertia • a property of matter that opposes any change in its state of motion • Newton’s First Law

  9. Projectile An object propelled through the air, especially one thrown as a weapon

  10. Projectile Motion • The process of movement horizontally and vertically simultaneously. • The components are independent of one another

  11. Types of Projectile Motion . http://www.glenbrook.k12.il.us/gbssci/Phys/Class/usage.html

  12. Two Components of Projectile Motion • Horizontal Motion • Vertical Motion • THEY ARE INDEPENDENT OF ONE ANOTHER!!!!!!!!

  13. How would you describe the trajectory? Parabolic

  14. http://www.glenbrook.k12.il.us/gbssci/Phys/Class/usage.html

  15. Suppose you shoot a gun a drop a spare bullet at the same time. • Who lands first?

  16. Projectiles. From Physclips: Mechanics with animations and film. • View the independence of vertical and horizontal motion • Ballistics cart demo

  17. Show Mythbusters gun video here • If time permits

  18. EX 1 A cannon ball is shot from a cannon with a horizontal velocity of 20m/s. What is the vertical and horizontal displacement after 1 second? After 2 seconds ?

  19. Vertical displacement:What do you know? d = vi = vf = a = t = horizontal velocity of 20m/s

  20. Vertical displacement:What do you know? d = vi = 0 m/s vf = a = 9.8 m/s2 t = 1sec Which formula wouldyou use to solve for d? dy = viy t + ½ ay t2 horizontal velocity of 20m/s

  21. To calculate vertical displacementONLY USE VERTICAL INFO ! dy = viy t + ½ ay t2 Whatisviy t = to? dy = ½ ay t2 Where: dy = vertical displacement (y axis) ay= g = gravity (9.8m/s2) (sometexts use negative to indicatedownward. Wewill assume gravity to be positive.) t = time in seconds

  22. Horizontal displacement (aka range):What do you know? d = vi = vf = a = t = horizontal velocity of 20m/s

  23. Horizontal displacement:What do you know? d = vi = 20 m/s vf = 20 m/s a = 0 m/s t = We will use 1s and 2 sec Which formula would you use to solve for d? dx = vix t + ½ ax t2 horizontal velocity of 20m/s

  24. Of these three equations, the top equation is the most commonly used. The other two equations are seldom (if ever) used. An application of projectile concepts to each of these equations would also lead one to conclude that any term with ax in it would cancel out of the equation since ax = 0 m/s/s.

  25. To calculate horizontal displacement. ONLY USE HORIZONTAL INFO ! Time determined vertically. dx = vi t + ½ a t2 Since a is zero, then ½ a t2 = zero dx = vix* t d = vt Where: dx = horizontal displacement (x axis) The subscript x refers to horizontal Vix = initial horizontal velocity t = time in seconds

  26. Calculate the displacement at 2 seconds

  27. How does vertical displacement change as time increases? How does horizontal displacement change as time increases?

  28. EX 2 • A ball is thrown horizontally at 25 m/s off a roof 15 m high. • A. How long is this ball in flight? • B. How far does the ball travel vertically? • C. How far does the ball travel horizontally (range)? • How would I calculate final velocity horizontal? Vertical?

  29. How long is it in the air? d = vit + .5at2 Since vi= 0, this can be simplified to: d = .5at2 To solve for t: t = d/.5a 1.75 sec

  30. Using time from vertical motion, can calculate distance for horizontal motion dx = vi t + ½ a t2 Since a is zero, then ½ a t2 = zero dx = vix* t d = vt 43.8m

  31. 2 Objects are dropped from a height of 10 m. Object A has a mass of 50 g. Object B has a mass of 100g. If there is no air friction, then: • A. Object A should hit the ground before Object B • B. Object B should hit the ground before Object A • C. Object A and Object B should hit the ground at the same time.

  32. 10/6 • Tests are not graded • We are continuing with PM today

  33. EX 3

  34. d = vt d / t = v 20 m / 1.01 s = v 19.8 m/s = v d = .5 at2 1.01 s = t

  35. EX 4A projectile is shot with a speed of 39.5 m/s straight off a roof and lands 198 m away. From what elevation was it shot? ? With what speed does it impact the ground vertically and horizontally? With what overall velocity does it impact the ground? d = vt d / v = t 198 m / 39.5 m/s = t 5.01 s = t d = ½ at 2 d = ½(9.8 m/s2)(5.01)2 d = 123 m

  36. EX 4A projectile is shot with a speed of 39.5 m/s straight off a roof and lands 198 m away. From what elevation was it shot? ? With what speed does it impact the ground vertically and horizontally? With what overall velocity does it impact the ground? vxf = 39.5 m/s vyf = at vyf = (9.8 m/s2)(5.01) vyf = 49.1 m/s vr= √(49.1 m/s)2 + (39.5 m/s)2 vr= 63.0 m/s

  37. EX 5 A projectile is shot horizontally off a 267-m tall building with a speed of 14.3 m/s. A. With what speed does it impact the ground vertically and horizontally? B. With what overall velocity does it impact the ground?

  38. vf horizontal is constant at 14.3 m/s • vf2 = vi2 + 2ax to determine vf vertically • vfy = 72.3 m/s • overall velocity? • This is just determining the resultant using Pythagoreans • vr2 = (14.3 m/s)2 + (72.3m/s)2 • vr = 73.7 m/s

  39. Example 6: A projectile is thrown upward at a rate of 13.22 m/s and at an angle of 83.1° with the horizontal. A. How long is the projectile in the air? B. Calculate the range. C. What is the peak height?

  40. Projectiles at a known velocity and angleSteps to determine time, height , and range 1. Determine X component (C=A/H) This yields the horizontal vi and vf 2. Determine Y component (S=O/H) This yields the vertical up vi and vertical down vf 3. Make 3 column table of knowns: Horizontal, Vertical Up, and Vertical down Remember horizontal acceleration = 0; vertical acceleration is 9.8 m/s2 due to gravity 4. Calculate peak time using vertical down column vf = vi + at 5. Total time in air (horizontal) is 2 x peak time 6. Calculate peak height using vertical information x = .5at2 (vi t = 0 in vertical down column) 7. Calculate range using horizontal information x = vi t (.5at2 = 0)

  41. What can you say about a trajectory path?

  42. Example 6: A projectile is thrown upward at a rate of 13.22 m/s and at an angle of 83.1° with the horizontal. Indicate knowns

  43. How do we determine the initial velocities? Given 13.22 m/s at an angle of 83.1° This describes the resultant of the horizontal and vertical velocity components. You need to determine the horizontal and vertical components

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