Announcement. Quiz on Friday (Graphing and Projectile Motion) No HW due Wednesday
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1 Going over HW3.05
2 Announcement Quiz on Friday (Graphing and Projectile Motion) No HW due Wednesday
3 As the red ball rolls off the edge, a green ball is dropped from rest from the same height at the same time Which one will hit the ground first? They will hit at the SAME TIME!!!
4 Projectile Motion Objective: 1. To view projectile motion as a result of vector independence
5 The same time?!? How?!? The red ball has an initial HORIZONTAL velocity (v ix ) But does not have any initial VERTICAL velocity (v iy = 0) The green ball falls from rest and has no initial velocity IN EITHER DIRECTION! v iy and v ix = 0 v ix
6 One Dimension at a Time Both balls begin with no VERTICAL VELOCITY Both fall the same VERTICAL DISTANCE Both fall with the same ACCELERATION This means that the time of flight IS THE SAME IN BOTH CASES Sideways motion has no influence on time of flight (only height does)
7 MythBusters Video How does this actually look in real life?
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11 Day 2 Projectile Motion
12 Horizontally-Launched projectiles In the x-direction, it has constant velocity In the y-direction, it is in free fall (9.8m/s/s) The x and y components have absolutely no affect on each other! (This is called the independence of vectors) The time it takes for an object to fall completely depends on its height, not horizontal velocity.
13 Announcements Unit Exam on Kinematics next Thursday No quiz on Friday No homework due Friday
14 Regents Practice: Projectile Motion
15 The diagram below represents the path of an object after it was thrown. What happens to the object s acceleration as it travels from A to B? A. It decreases. B. It increases. C. It remains the same. D. It depends on how fast the object was thrown
16 The diagram below represents the path of an object after it was thrown. What happens to the object s acceleration as it travels from A to B? A. It decreases. B. It increases. C. It remains the same. D. It depends on how fast the object was thrown
17 A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is A. one-half as great B. twice as great C. the same D. four times as great
18 A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is A. one-half as great B. twice as great C. the same D. four times as great
19 An object was projected horizontally from a tall cliff. The diagram to the right represents the path of the object, neglecting friction. 1. How does the magnitude of the horizontal component of the object s velocity at A compare with the magnitude of the horizontal component of the object s velocity at point B? EXPLAIN. 2. How does the magnitude of the vertical component of the object s velocity at point A compare with the magnitude of the vertical component of the object s velocity at point B? EXPLAIN.
20 An object was projected horizontally from a tall cliff. The diagram to the right represents the path of the object, neglecting friction. The horizontal component remains unchanged (no acceleration) 1. How does the magnitude of the horizontal component of the object s velocity at A compare with the magnitude of the horizontal component of the object s velocity at point B? EXPLAIN. The vertical component is increasing (vertically faster, a = 9.8 m/s/s) 2. How does the magnitude of the vertical component of the object s velocity at point A compare with the magnitude of the vertical component of the object s velocity at point B? EXPLAIN.
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22 independent 9.8m/s/s 0 downward Horizontal velocity
23 horizontal horizontal
24 horizontal horizontal
25 Day 2 Angled Launch Objective: To determine which launch angles result in maximum height, range, and time of flight
26 Activity: Experimenting with different Launch Angles Greatest Height? Farthest Range? Maximum time of flight? How would all of this change if we had air resistance? Symmetry about 45º
27 A projectile launched at an angle of 45 above the horizontal travels through the air. Compared to the projectile s theoretical path with no air friction, the actual trajectory of the projectile with air friction is A. lower and shorter B. lower and longer C. higher and shorter D. higher and longer
28 A projectile launched at an angle of 45 above the horizontal travels through the air. Compared to the projectile s theoretical path with no air friction, the actual trajectory of the projectile with air friction is A. lower and shorter B. lower and longer C. higher and shorter D. higher and longer
29 A golf ball is hit at an angle of 45 above the horizontal. What is the acceleration of the golf ball at the highest point in its trajectory? [Neglect friction.] A. 9.8 m/s 2 upward B. 9.8 m/s 2 downward C. 6.9 m/s 2 horizontal D. 0.0 m/s 2
30 A golf ball is hit at an angle of 45 above the horizontal. What is the acceleration of the golf ball at the highest point in its trajectory? [Neglect friction.] A. 9.8 m/s 2 upward B. 9.8 m/s 2 downward C. 6.9 m/s 2 horizontal D. 0.0 m/s 2
31 Try out HW3.06 I am not assigning it just yet. Tomorrow we learn how to do Quantitative projectile motion problems and then you will work on 3.06 in class on Friday
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35 Day 3 - Quantitative PM
36 Projectile Motion - Quantitative Objective: To be able to solve PM problems involving actual quantities
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38 Which forces are acting in the x and y directions? [Neglect air resistance]
39 Which forces are acting in the x and y directions? [Neglect air resistance] Y-direction: Net force = gravity -> gravitational acceleration (ay = 9.8m/s/s) X-direction: No net force -> no acceleration (ax = 0 m/s/s; neglect air resistance)
40 X and Y have no effect on each other!
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42 The time it takes to fall depends on height, not horizontal velocity
43 Note: This is also called the range.
44 Use displacement equation in each dimension
45 Assume a horizontal launch.
46 t = 1.75 x = 35m
47 1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile? b. How far away from the bottom of the ledge does the ball land?
48 1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile? 2.02 s b. How far away from the bottom of the ledge does the ball land? 50.5 m
49 2. A bomb is released from a plane flying level at an altitude of m. It lands m horizontally from where it was released. a. How long was the bomb in the air? b. What was the plane's speed when the bomb was released?
50 2. A bomb is released from a plane flying level at an altitude of m. It lands m horizontally from where it was released. a. How long was the bomb in the air? s b. What was the plane's speed when the bomb was released? m/s
51 3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff? b. How far away does the stone hit the ground?
52 3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff? 988 m b. How far away does the stone hit the ground? 355 m
53 4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the water below? b. How far from the base of the bridge will it hit?
54 4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the water below? 5.53 s b. How far from the base of the bridge will it hit? 33.2 m
55 5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air? b. How high was it thrown from?
56 5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air? 3 s b. How high was it thrown from? 44 m
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