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2D-Motion

Introduction

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Chapter 3. Reading QuizzesChapter 3. Reading Quizzes

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What is a vector?

A. A quantity having both size and directionB. The rate of change of velocityC. A number defined by an angle and a

magnitudeD. The difference between initial and final

displacementE. None of the above

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What is a vector?

A. A quantity having both size and directionB. The rate of change of velocityC. A number defined by an angle and a

magnitudeD. The difference between initial and final

displacementE. None of the above

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What is the name of the quantity represented as ?

A. Eye-hatB. Invariant magnitudeC. Integral of motionD. Unit vector in x-directionE. Length of the horizontal axis

i

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A. Eye-hatB. Invariant magnitudeC. Integral of motionD. Unit vector in x-directionE. Length of the horizontal axis

What is the name of the quantity represented as ?i

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This chapter shows how vectors can be added using

A. graphical addition.B. algebraic addition.C. numerical addition.D. both A and B.E. both A and C.

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A. graphical addition.B. algebraic addition.C. numerical addition.D. both A and B.E. both A and C.

This chapter shows how vectors can be added using

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To decompose a vector means

A. to break it into several smaller vectors.B. to break it apart into scalars.C. to break it into pieces parallel to the axes.D. to place it at the origin.E. This topic was not discussed in Chapter 3.

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A. to break it into several smaller vectors.B. to break it apart into scalars.C. to break it into pieces parallel to the axes.D. to place it at the origin.E. This topic was not discussed in Chapter 3.

To decompose a vector means

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Chapter 3. Concept QuestionsChapter 3. Concept Questions

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Which figure shows ? A A A1 2 3

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Which figure shows ? A A A1 2 3

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Which figure shows 2 − ?A

B

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Which figure shows 2 − ?A

B

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What are the x- and y-components Cx and Cy of vector ?

C

A. Cx = 1 cm, Cy = –1 cmB. Cx = –3 cm, Cy = 1 cmC. Cx = –2 cm, Cy = 1 cmD. Cx = –4 cm, Cy = 2 cmE. Cx = –3 cm, Cy = –1 cm

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What are the x- and y-components Cx and Cy of vector ?

C

A. Cx = 1 cm, Cy = –1 cmB. Cx = –3 cm, Cy = 1 cmC. Cx = –2 cm, Cy = 1 cmD. Cx = –4 cm, Cy = 2 cmE. Cx = –3 cm, Cy = –1 cm

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Chapter 4. Reading Quizzes

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A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a

A. tangential curve. B. sine curve. C. parabolic curve.D. linear curve.

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A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a

A. tangential curve. B. sine curve. C. parabolic curve.D. linear curve.

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A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently,

A. the bullet passes above the coconut. B. the bullet hits the coconut.C. the bullet passes beneath the coconut. D. This wasn’t discussed in Chapter 4.

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A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently,

A. the bullet passes above the coconut. B. the bullet hits the coconut.C. the bullet passes beneath the coconut. D. This wasn’t discussed in Chapter 4.

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Projectile Motion

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2D Motion Concept Questions2D Motion Concept Questions

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A. slow down and curve downward.B. slow down and curve upward.C. speed up and curve downward.D. speed up and curve upward.E. move to the right and down.

This acceleration will cause the particle to

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A. slow down and curve downward.B. slow down and curve upward.C. speed up and curve downward.D. speed up and curve upward.E. move to the right and down.

This acceleration will cause the particle to

Firing Balls I

A small cart is rolling at

constant velocity on a flat

track. It fires a ball straight

up into the air as it moves.

After it is fired, what

happens to the ball?

1) it depends on how fast the cart 1) it depends on how fast the cart is movingis moving

2) it falls behind the cart2) it falls behind the cart

3) it falls in front of the cart3) it falls in front of the cart

4) it falls right back into the cart4) it falls right back into the cart

5) it remains at rest5) it remains at rest

ConcepTest 3.4a Firing Balls I

A small cart is rolling at

constant velocity on a flat

track. It fires a ball straight

up into the air as it moves.

After it is fired, what happens

to the ball?

1) it depends on how fast the cart 1) it depends on how fast the cart is movingis moving

2) it falls behind the cart2) it falls behind the cart

3) it falls in front of the cart3) it falls in front of the cart

4) it falls right back into the cart4) it falls right back into the cart

5) it remains at rest5) it remains at rest

when viewed from

train

when viewed from

ground

In the frame of reference of the cart, the ball only has a verticalvertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocitysame horizontal velocity, so the ball still returns into the cart.

Dropping a Package

You drop a package from You drop a package from

a plane flying at constant a plane flying at constant

speed in a straight line. speed in a straight line.

Without air resistance, Without air resistance,

the package will:the package will:

1) quickly lag behind the plane quickly lag behind the plane while fallingwhile falling

2) remain vertically under the 2) remain vertically under the plane while fallingplane while falling

3) move ahead of the plane 3) move ahead of the plane while fallingwhile falling

4) not fall at all4) not fall at all

You drop a package from You drop a package from

a plane flying at constant a plane flying at constant

speed in a straight line. speed in a straight line.

Without air resistance, Without air resistance,

the package will:the package will:

1) quickly lag behind the plane quickly lag behind the plane while fallingwhile falling

2) remain vertically under the 2) remain vertically under the plane while fallingplane while falling

3) move ahead of the plane 3) move ahead of the plane while fallingwhile falling

4) not fall at all4) not fall at all

Both the plane and the package have the

samesame horizontalhorizontal velocityvelocity at the moment of

release. They will maintainmaintain this velocity in

the xx-direction-direction, so they stay aligned.

Follow-up:Follow-up: What would happen if air resistance were present? What would happen if air resistance were present?

ConcepTest 3.5 Dropping a Package

Dropping the Ball I

From the same height (and

at the same time), one ball

is dropped and another

ball is fired horizontally.

Which one will hit the

ground first?

1) the “dropped” ball1) the “dropped” ball

2) the “fired” ball2) the “fired” ball

3) they both hit at the same time3) they both hit at the same time

4) it depends on how hard the 4) it depends on how hard the ball was firedball was fired

5) it depends on the initial height5) it depends on the initial height

1) the “dropped” ball1) the “dropped” ball

2) the “fired” ball2) the “fired” ball

3) they both hit at the same time3) they both hit at the same time

4) it depends on how hard the 4) it depends on how hard the ball was firedball was fired

5) it depends on the initial height5) it depends on the initial height

Both of the balls are falling vertically under the influence of gravity.

They both fall from the same heightThey both fall from the same height.. Therefore, they will hit the Therefore, they will hit the

ground at the same time.ground at the same time. The fact that one is moving horizontally

is irrelevant – remember that the x and y motions are completely

independent !!

Follow-up:Follow-up: Is that also true if there is air resistance? Is that also true if there is air resistance?

Dropping the Ball I

From the same height (and

at the same time), one ball

is dropped and another ball

is fired horizontally. Which

one will hit the ground

first?

Dropping the Ball II

In the previous problem, In the previous problem,

which ball has the greater which ball has the greater

velocity at ground level?velocity at ground level?

1) the “dropped” ball1) the “dropped” ball

2) the “fired” ball2) the “fired” ball

3) neither – they both have the 3) neither – they both have the

same velocity on impactsame velocity on impact

4) it depends on how hard the 4) it depends on how hard the

ball was thrownball was thrown

In the previous problem, In the previous problem,

which ball has the greater which ball has the greater

velocity at ground level?velocity at ground level?

1) the “dropped” ball1) the “dropped” ball

2) the “fired” ball2) the “fired” ball

3) neither – they both have the 3) neither – they both have the

same velocity on impactsame velocity on impact

4) it depends on how hard the 4) it depends on how hard the

ball was thrownball was thrownBoth balls have the same same verticalvertical velocity 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 “fired” ball has a larger net velocityvelocity when it hits the ground.

Dropping the Ball II

Projectile

A projectile is launched

from the ground at an angle

of 30o. At what point in its

trajectory does this

projectile have the least

speed?

1) just after it is launched

2) at the highest point in its flight

3) just before it hits the ground

4) halfway between the ground and

the highest point

5) speed is always constant

A projectile is launched

from the ground at an

angle of 30o. At what point

in its trajectory does this

projectile have the least

speed?

1) just after it is launched

2) at the highest point in its flight

3) just before it hits the ground

4) halfway between the ground and

the highest point

5) speed is always constantThe speed is smallestsmallest at the

highest pointhighest point of its flight path

because the yy-component of -component of

the velocity is zerothe velocity is zero.

Projectile