1. Chapter 3.3-3.4 Review

2. 1. Two forces are applied to a stump by two tractors. One is a 150 N force to the east. The other is 100 N in a direction 35° north of east. What is the resultant force?

3. sin35° = F north /100 F north = 57 N north cos35° = F east /100 F east = 82 N east

4. 150 N east + 82 N east = 232 N east 232 2 + 57 2 = c 2 c = 238 N tan  = 57/238 13.5°  north of east

5. 2. A jogger runs 1200 m in a direction 65° south of west. He then runs 1300 m west. What is his total displacement?

6. sin65° = S /1200 S = 1088 m south cos65° = W/1200 W = 507 m west

7. 1300 m west + 507 m west = 1807 m west 1807 2 + 1088 2 = c 2 c = 2109 m tan  = 1088/1807 31°  south of west

8. 3. An Aggie pushes his car with a force of 500 N. Because he forgot to release the parking brake, the ground pushes on the car with a force of 500 N in the opposite direction. What is the net force on the car?

9. 0, the net force is 500 N + (–500 N) = 0 N

10. 4. What are the components of projectile motion? What shape does the path of an object in projectile motion take?

11. The components of projectile motion are initial horizontal velocity, object only under the force of gravity, and no air resistance. The shape of the path is a parabola.

12. 5. Why don’t projectiles on earth really follow the path of a parabola?

13. Air resistance slows the object.

14. 6. Which of these objects are in projectile motion? A. a rocket being launched B. a thrown baseball C. a cat jumping down from the roof D. a wheel falling from the landing gear of an airplane E. a pecan nut falling off the limb of a pecan tree F. a leaf falling from a tree G. a rock sinking through the water in a pond H. a flying paper airplane

15. 6. Which of these objects are in projectile motion? B. a thrown baseball C. a cat jumping down from the roof D. a wheel falling from the landing gear of an airplane E. a pecan nut falling off the limb of a pecan tree (All the others have some other force on them.)

16. 7. Which of the choices above move with a parabolic motion?

17. 7. Which of the choices above move with a parabolic motion? B. a thrown baseball C. a cat jumping down from the roof D. a wheel falling from the landing gear of an airplane (If it is in projectile motion it follows a parabola, except for the pecan nut which has no horizontal velocity.)

18. 8. A bag of flour falls from an airplane flying level at 150 m/s at a height above the ground of 290 m. How long does it take the bag to fall to the ground?

19. y = v 0 t + ½ gt 2 290 = ½ 10(t) 2 t = 7.6 s

20. 9. With what vertical velocity does the bag in question 8 hit the ground?

21. v = v 0 + gt v = 0 + 10(7.6) v = 76 m/s

22. 10. With what horizontal velocity does the bag in question 8 hit the ground?

23. 150 m/s The horizontal velocity doesn’t change as it falls.

24. 11. With what velocity does the bag in question 8 hit the ground? Don’t forget direction!

25. 150 2 + 76 2 = c 2 c = 168 m/s tan  = 76/150 27°  below horizontal

26. 12. How far does the bag in question 8 travel horizontally before it hits the ground?

27. 150 m/s x 7.6 s = 1140 m

28. 13. A bullet is fired at a velocity of 1000 m/s at an angle of 22° to the ground. What is the vertical component of the bullet’s velocity?

29. sin22° = v v /1000 v v = 375 m/s

30. 14. How long is the bullet in question 13 in the air?

31. v = v 0 + gt 0 = 375 + (-10)t t = 37.5 s 37.5 s x 2 = 75 s

32. 15. What is the horizontal velocity of the bullet in question 13?

33. cos22° = v h /1000 v h = 927 m/s

34. 16. How far does the bullet in question 13 travel before hitting the ground?

35. 927 m/s x 75 s = 69525 m

36. 17. An athlete in the shot put competition launches a shot at an angle of 50° to the ground. The initial velocity of the shot is 14 m/s. What distance does the shot travel before hitting the ground?

37. sin50° = v v /14 v v = 10.7 m/s

38. v = v 0 + gt 0 = 10.7 + (-10)t t = 1.07 s 1.07 s x 2 = 2.14 s

39. cos50° = v h /14 v h = 9 m/s

40. 9 m/s x 2.14 s = 19.26 m

41. 18. You are riding in a car moving 35 m/s to the east. You are tossing a ball straight up and catching it as it falls. Describe the velocity of the ball from your perspective.

42. The ball appears to move straight up and straight down.

43. 19. Describe the velocity of the ball in question 18 as viewed by a pedestrian standing at the side of the road as your car passes.

44. It appears to follow a parabola on each toss.

45. 20. A car slowly rolls off a cliff and falls 230 meters to the river below. How long does it take the car to fall to the water? How long does it take the car to fall if it has an initial horizontal velocity of 40 m/s?

46. y = v 0 t + ½ gt 2 230 = ½ 10(t) 2 t = 6.8 s

47. t = 6.8 s Horizontal velocity doesn’t affect the vertical motion.