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- 1. A Projectile Fired at an Angle A conceptual study
- 2. When an object is dropped, the only thing that is affecting its motion is gravity, g .
- 3. When an object is dropped, the only thing that is affecting its motion is gravity, g . Gravity is a force, F .
- 4. When an object is dropped, the only thing that is affecting its motion is gravity, g . Gravity is a force, F . Newton says that a force causes a mass, m , to accelerate:
- 5. So, when an object is dropped, it starts from rest (v i = 0 m/s), and it accelerates at ~+10 m/s each second.
- 6. So, when an object is dropped, it starts from rest (v i = 0 m/s), and it accelerates at ~+10 m/s each second. So, each second, the object is traveling 10 m/s faster than it was the second before.
- 7. Also, since the object is accelerating, it will travel a greater distance each second than it did the second before.
- 8. Also, since the object is accelerating, it will travel a greater distance each second than it did the second before. So, it’s obvious that, the longer an object falls, the faster it will go and the farther it will fall.
- 9. Let’s consider an object that’s thrown straight up. It goes up and then slows to a stop. At its highest point, its instantaneous velocity is 0 m/s. It then starts downward as if dropped from rest at that height. 0 m/s
- 10. During the upward part of the motion, the object slows from its initial upward velocity, v i , to 0 velocity. 0 m/s - g + g -v i +v i
- 11. During the upward part of the motion, the object slows from its initial upward velocity, v i , to 0 velocity. 0 m/s - g + g -v i +v i We know its accelerating because its velocity is changing.
- 12. During the upward part of the motion, the object slows from its initial upward velocity, v i , to 0 velocity. 0 m/s - g + g -v i +v i We know its accelerating because its velocity is changing. Since it’s decreasing in velocity, we say it’s accelerating negatively.
- 13. Each second, it is moving at 10 m/s slower than it was the second before. 0 m/s -40 m/s -30 m/s -20 m/s -10 m/s 40 m/s 30 m/s 20 m/s 10 m/s
- 14. Each second, it is moving at 10 m/s slower than it was the second before. 0 m/s -40 m/s -30 m/s -20 m/s -10 m/s 40 m/s 30 m/s 20 m/s 10 m/s Once it reaches the top and begins to fall back, it is moving at 10 m/s faster each second.
- 15. Each second, it is moving at 10 m/s slower than it was the second before. 0 m/s -40 m/s -30 m/s -20 m/s -10 m/s 40 m/s 30 m/s 20 m/s 10 m/s Once it reaches the top and begins to fall back, it is moving at 10 m/s faster each second. Whether moving up or down, the object accelerates at the same rate…10 m/s 2 .
- 17. Now, let’s consider objects that are thrown up and horizontally at the same time, a projectile fired at an angle.
- 18. Now, let’s consider objects that are thrown up and horizontally at the same time, a projectile fired at an angle. The objects’ vertical and horizontal motions are completely independent of each other.
- 19. The object will move vertically exactly the same as it would if thrown straight up. Vertical motion Horizontal motion
- 20. The object will move vertically exactly the same as it would if thrown straight up. It will move horizontally just like it would if it were rolling across a smooth, level, surface. Vertical motion Horizontal motion
- 21. It will accelerate vertically. It will move at a constant velocity horizontally. g v
- 22. Let’s say Kyle threw a ball at some velocity, v , at 60 ° above the horizontal. 60 ° v
- 23. Let’s say Kyle threw a ball at some velocity, v , at 60 ° above the horizontal. 60 ° v The thrown ball is moving upward and horizontally at the same time.
- 24. Let’s say Kyle threw a ball at some velocity, v , at 60 ° above the horizontal. 60 ° v The thrown ball is moving upward and horizontally at the same time. The ball has an initial vertical velocity, v y . v y
- 25. Let’s say Kyle threw a ball at some velocity, v , at 60 ° above the horizontal. 60 ° v The thrown ball is moving upward and horizontally at the same time. The ball has an initial vertical velocity, v y . v y It also has an initial horizontal velocity, v x . v x
- 26. v y = v sin 60 ° v v y v x
- 27. v y = v sin 60 ° v v y v x v x = v cos
- 28. v y = v sin 60 ° v = 50 m/s v y v x v x = v cos Let’s say Kyle through the ball at 50 m/s. Not bad!
- 29. v y = v sin 60 ° v = 50 m/s v y v x v x = v cos Let’s say Kyle through the ball at 50 m/s. Not bad! So what’s the horizontal and vertical velocities of the throw?
- 30. 60 ° v = 50 m/s v y = 43 m/s v x
- 31. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s
- 32. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the horizontal velocity as time passes?
- 33. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the horizontal velocity, v x , as time passes? Nothing! There is no horizontal force, therefore, no horizontal acceleration.
- 34. v x v x v x v x v x v x v x v x v x
- 35. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the vertical velocity, v y , as time passes?
- 36. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the vertical velocity, v y , as time passes? It should decrease until it reaches the top of its flight, then increase as it falls.
- 37. v y v y v y v y v y v y v y v y v y = 0
- 38. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the vertical acceleration as time passes?
- 39. 60 ° v = 50 m/s v y = 43 m/s v x = 25 m/s What should happen to the vertical acceleration as time passes? Nothing. Acceleration is gravity, g , and remains at 10 m/s 2 .
- 40. g = 10 m/s g g g g g g g g

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