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UNIT 2 Two Dimensional Motion And Vectors 1

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ConcepTest 3.5 Dropping a Package You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: quickly lag behind the plane while falling 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all 2

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ConcepTest 3.5 Dropping a Package You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: quickly lag behind the plane while falling 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all same horizontal velocity maintain x-direction Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x-direction, so they stay aligned. Follow-up: What would happen if air resistance is present? 3

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ConcepTest 3.6bDropping the Ball II In the previous problem, which ball has the greater velocity at ground level? 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown 4

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ConcepTest 3.6bDropping the Ball II In the previous problem, which ball has the greater velocity at ground level? 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown same vertical velocity “fired” ball has a larger net velocity Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? 5

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Monday September 26 Projectiles: Launch At Any Angle 6

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TODAY’S AGENDA Projectile Motion Mini-Lesson: Launch At Any Angle Hw: Complete Practice D Problems (all) UPCOMING… Tues:LAB 3: Projectile Motion Wed:More Projectile Motion the Boards Fri:Problem Quiz 2 Projectile Motion Access to Reading Quizzes 11:30pm the Boards Tues:CH 3 TEST Monday, September 26 7

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8 Demonstration with Dr. Walter Lewin Demonstration with MythBusters

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9 General Launch Angle

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10 General Launch Angle

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11 Resolving the Velocity

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12 Resolving the Velocity

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13 Projectile Motion Equations Eq 1 Horizontal Velocity Eq 2 Vertical Velocity Eq 4 Horizontal Displacement Eq 3

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14 Eq 6Range Projectile Motion Equations Eq 5 Vertical Displacement Eq 7 Time to the Top

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A golfer hits a golf ball at an angle of 25.0˚ to the ground. If the golf ball covers a horizontal distance of m, what is the ball’s maximum height? (Hint: At the top of its flight, the ball’s vertical velocity component will be zero.) Consider the Range equation: Solve for the Now find time to the top: Sample Problem 15

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Find the vertical height at 2.68 s : 16

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17 Sample Problem A potato is shot from a potato gun at m/s at an angle of 45.0˚. The potato is shot from a bridge 50.0 m above the water. Find the following: a) total time of flight b) final velocity just before hitting the water c) total horizontal displacement d) maximum vertical displacement above the water

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What must I do first? Break the initial velocity into x- and y- components. Which question is easiest to answer? Find the total time of flight Which equation has all the information but time? By quadratic equation, t = 15 s 18

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Without the quadratic formula solve for t: i.Find final velocity in y-axis ii.Find time 2 STEPS: 19

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What is the final velocity? 20

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What is the total horizontal displacement? What is the maximum vertical displacement above the water? 21

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22 Sample Problem.82 s

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