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Chapter 5 Projectile motion

Chapter 5 Projectile motion. Chapter 4: straight line motion that was ONLY vertical or ONLY horizontal motion. Chapter 5: considers motion that follows a diagonal path or a curved path. When you throw a baseball, the trajectory is a curved path.

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Chapter 5 Projectile motion

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  1. Chapter 5 Projectile motion

  2. Chapter 4: straight line motionthat was ONLY vertical or ONLY horizontal motion

  3. Chapter 5: considers motion that follows a diagonal path or a curved path

  4. When you throw a baseball,the trajectory is a curved path.

  5. We are going to separate the motion of a projectile into independent x and y motions

  6. The vertical motion is not affected by the horizontal motion. And the horizontal motion is not affected by the vertical motion.

  7. Observe: a large ball bearing is dropped at the same time as a second ball bearing is fired horizontally.

  8. What happened?

  9. Remember adding 2 perpendicular vectorshorizontal and vertical vectors.

  10. When we add perpendicular vectors we use Pythagorean theorem to find the resultant.

  11. Consider a vector B that is pointed at an angle q wrt horizontal direction.

  12. We are going to break vector B into 2 perpendicular vectors: Bx and By

  13. if you ADD vectors Bx + By you get vector B.

  14. Graphically, we can say:

  15. Draw a rectangle with vector B as the diagonal. the component vectorsBx and By are the sides of the rectangle

  16. Application:

  17. A Boat in a river

  18. How can we describe the motion of a boat in a river?

  19. The motion is affected by the motor of the boat and by the current of the river

  20. Imagine a river 120 meters wide with a current of 8 m/sec.

  21. Imagine a river 120 meters wide with a current of 8 m/sec.

  22. If a boat is placed in the river [motor is off] , how fast will the boat drift downstream?

  23. If the boat is drifting, the total speed of the boat just equals the speed of the current.

  24. for a boat drifting with the current: Vtotal= Vboat + VcurrentVtotal = -0 + Vcurrent = 8 m/sec

  25. Now suppose this boat can travel at a constant 15 m/sec when the motor is on .

  26. What is the total speed of the boat downstream when the motor is on?

  27. The boat is traveling in the same direction as the current.

  28. V total downstream = Vtotal = Vboat + VcurrentVtotal = 15↓ + 8↓ = 23 m/sec ↓

  29. What is the total speed of the boat traveling upstream[against the current] ?

  30. The boat and current now move in opposite directions

  31. Vtotal = Vboat +VcurrentVtotal = 15 ↓+ ( 8 ↑) Vtotal = 7↓ m/sec

  32. Summary:traveling downstream: Vboat + VcurrentTraveling upstream:Vboat + [-Vcurrent]

  33. Crossing the river.

  34. If there was no current, how many seconds needed for this boat to travel 120 meters from A to B?

  35. Velocity = distance timeso time = distance velocity

  36. time = distance velocitytime = 120 m 15 m/sectime = 8 seconds

  37. But there if IS a current. what happens when you try to go straight across the river from A to B?

  38. The boat will travel from A to C.

  39. Every second the boat travels ACROSS 15 meters and AT THE SAME TIMEevery secondthe boat will be pushedDOWNSTREAm 8 meters by the current .

  40. Vboat = 15  and Vcurrent = 8↓These velocities are perpendicular

  41. The RESULTANT velocity of the boat is

  42. Vresultant2 = Vboat2 + Vcurrent2Vresultant2 = 152+ 82Vresultant2 = 225+ 64 =289Vresultant = 17 m/sec

  43. The boat still crosses the river in 8 seconds , but it lands downstream at point C not at point B.

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