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UNIT 2Two Dimensional Motion

And Vectors

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:

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

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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:

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

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

ConcepTest 3.6b Dropping 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

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ConcepTest 3.6b Dropping 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

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?

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Monday September 26

Projectiles: Launch At Any Angle

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TODAY’S AGENDA

Projectile MotionMini-Lesson: Launch At Any AngleHw: Complete Practice D Problems (all)

UPCOMING…

Tues: LAB 3: Projectile Motion Wed: More Projectile Motion Thurs: Problems @ the Boards Fri: Problem Quiz 2 Projectile Motion

Access to Reading Quizzes ENDS @ 11:30pm Mon: Problems @ the Boards Tues: CH 3 TEST

Monday, September 26

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Demonstration with Dr. Walter Lewin

Demonstration with MythBusters

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General Launch Angle

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General Launch Angle

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Resolving the Velocity

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Resolving the Velocity

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Projectile Motion Equations

Eq 1Horizontal Velocity

Eq 2Vertical Velocity

Eq 4Horizontal Displacement

Eq 3

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Eq 6Range

Projectile Motion Equations

Eq 5Vertical Displacement

Eq 7Time 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 301.5 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

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Find the vertical height at 2.68 s:

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Sample Problem

A potato is shot from a potato gun at 100.0 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 flightb) final velocity just before hitting the waterc) total horizontal displacementd) 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

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Without the quadratic formula solve for t:

i. Find final velocity in y-axisii. Find time

2 STEPS:

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What is the final velocity?

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What is the total horizontal displacement?

What is the maximum vertical displacement above the water?

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Sample Problem

.82 s

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END