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Ch 03 HWCh 03 HW

Due: 9:30am on Monday, February 15, 2016Due: 9:30am on Monday, February 15, 2016

YYou will receive ou will receive no credit for items you complete ano credit for items you complete a ftfter the assignment is er the assignment is due.due. Grading PolicyGrading Policy

Prelecture Video: VectorsPrelecture Video: Vectors

Click PlayClick Play to watch the video. Answer the ungraded questions in the video and the graded follow-up questions at right. to watch the video. Answer the ungraded questions in the video and the graded follow-up questions at right.

Part APart A

Which of the following is a vector quantity?Which of the following is a vector quantity?

Check all that apply.Check all that apply.

ANSWER: ANSWER:

CorrectCorrect

A A vectvect or is or is a a physicphysical al quanquantity tity containing both containing both a a magnitude and magnitude and a a diredirectction.ion.

Part BPart B

The sum of two vectors is the largest when the two vectors are _____.The sum of two vectors is the largest when the two vectors are _____.

ANSWER: ANSWER:

momentummomentum

velocityvelocity

displacementdisplacement

accelerationacceleration

timetime

temperaturetemperature

forceforce

speedspeed

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CorrectCorrect

The sum of two vectors is the largest when the two vectors point in the same direction.The sum of two vectors is the largest when the two vectors point in the same direction.

Part CPart C

The sum of theThe sum of the x x components of components of vectors A and Bvectors A and B inin

is ___.is ___.

ANSWER: ANSWER:

CorrectCorrect

TheThe x x componecomponent nt of of the the resultant resultant of of two two vectvect ors ors is is ..

Part DPart D

Which of the choices shows the correct resultant of adding the twoWhich of the choices shows the correct resultant of adding the two vectors A and Bvectors A and B shown in ? shown in ?

pointing in the same directionpointing in the same direction

pointing in opposite directionspointing in opposite directions

perpendicular to each other perpendicular to each other

positioned at a 45° anglepositioned at a 45° angle

-5-5

1414

66

44

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ANSWER: ANSWER:

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CorrectCorrect

To find the resultant of two vectors, add them tail-to-tip and then draw the resultant vector from the tail of theTo find the resultant of two vectors, add them tail-to-tip and then draw the resultant vector from the tail of the

first vector to the tip of the last vector.first vector to the tip of the last vector.

Adding Adding and and Subtracting Vectors Subtracting Vectors Conceptual QuestionConceptual Question

Six vectors (A to F) have the magnitudes and directions indicated in the figure.Six vectors (A to F) have the magnitudes and directions indicated in the figure.

Part APart A

Which two vectors, when added, will have the largest (positive)Which two vectors, when added, will have the largest (positive) x x component? component?

Hint 1.Hint 1. LargestLargest x x component component

The two vectors with the largestThe two vectors with the largest x x components will, when combined, give the resultant with the largest components will, when combined, give the resultant with the largest x x

component. Keep in mind that positivecomponent. Keep in mind that positive x x components are larger than negative components are larger than negative x x components. components.

ANSWER: ANSWER:

CorrectCorrect

C and EC and E

E and FE and F

A A and Fand F

C and DC and D

B and DB and D

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Part BPart B

Which two vectors, when added, will have the largest (positive)Which two vectors, when added, will have the largest (positive) y y component? component?

Hint 1.Hint 1. LargestLargest y y component component

The two vectors with the largestThe two vectors with the largest y y components will, when combined, give the resultant with the largest components will, when combined, give the resultant with the largest y y

component. Keep in mind that positivecomponent. Keep in mind that positive y y components are larger than negative components are larger than negative y y components. components.

ANSWER: ANSWER:

CorrectCorrect

Part CPart C

Which two vectors, whenWhich two vectors, when subtracted subtracted (i.e., when one vector is subtracted from the other), will have the largest (i.e., when one vector is subtracted from the other), will have the largest

magnitude?magnitude?

Hint 1.Hint 1. Subtracting vectorsSubtracting vectors

To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectorsTo subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors

to the other vector.to the other vector.

ANSWER: ANSWER:

CorrectCorrect

± Vector Addition and Subtraction± Vector Addition and Subtraction

In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their

C and DC and D

A A and Fand F

E and FE and F

A A and Band B

E and DE and D

A A and Fand F

A A and Eand E

D and BD and B

C and DC and D

E and FE and F

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components. (You must first specify a coordinate system in order to find the components of each arrow.) This problemcomponents. (You must first specify a coordinate system in order to find the components of each arrow.) This problem

gives you some practice with the components.gives you some practice with the components.

Let Let vectvectors ors , , , , and and . . Calculate Calculate the the following, following, and and express express your your answeranswers s asas

ordered triplets of values separated by commas.ordered triplets of values separated by commas.

Part APart A

ANSWER: ANSWER:

CorrectCorrect

Part BPart B

ANSWER: ANSWER:

CorrectCorrect

Part CPart C

ANSWER: ANSWER:

CorrectCorrect

Part DPart D

ANSWER: ANSWER:

CorrectCorrect

Part EPart E

ANSWER: ANSWER:

== 3,-5,-43,-5,-4

== -5,4,0-5,4,0

== -6,4,3-6,4,3

== -3,-2,-11-3,-2,-11

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CorrectCorrect

Part FPart F

ANSWER: ANSWER:

CorrectCorrect

Tactics Box 3.1 Determining the Components of a Vector Tactics Box 3.1 Determining the Components of a Vector

Learning Goal:Learning Goal:

To practice Tactics Box 3.1 Determining the Components of a Vector.To practice Tactics Box 3.1 Determining the Components of a Vector.

When When a a vectvector or is is decompodecomposed sed intointo component vectorscomponent vectors and and parallel parallel to to the the coordinate coordinate axesaxes, , we we can can descdescriberibe

each component vector with a single number (a scalar) called theeach component vector with a single number (a scalar) called the component component . This tactics box describes how to. This tactics box describes how to

determine thedetermine the x x componecomponent nt and and y component y component of of vectvector or , , dendenoted oted and and ..

TACTICS BOX 3.1TACTICS BOX 3.1 Determining the components of a vector Determining the components of a vector

1. 1. The The absolute absolute value value of of thethe x x componencomponent t is is the the magnitude magnitude of of the the componecomponent nt vectvector or ..

2. The2. The signsign of of is is positivpositive e if if points points in in the the positivpositiv ee x x diredirectction; ion; it it is is negnegative ative if if points points in in thethe

negativenegative x x direction. direction.

3. The3. The y y componecomponent nt is is deterdetermined mined similsimilarlyarly..

Part APart A

What What is is the the magnitude magnitude of of the the componecomponent nt vectvector or shown shown in in the the figure?figure?

Express your answer in meters to one significant figure.Express your answer in meters to one significant figure.

== -11,14,8-11,14,8

== 17,-12,-617,-12,-6

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ANSWER: ANSWER:

CorrectCorrect

Part BPart B

What is the sign of theWhat is the sign of the y y componecomponent nt of of vectvector or shown shown in in the the figure?figure?

ANSWER: ANSWER:

CorrectCorrect

== 55

positivepositive

negativenegative

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Part CPart C

Now, combine the information given in the tactics box above to find theNow, combine the information given in the tactics box above to find the x x and and y y componecomponents, nts, and and , , of of

vectvector or shown shown in in the the figure.figure.

Express your answers, separated by a comma, inExpress your answers, separated by a comma, in

meters to one significant figure.meters to one significant figure.

ANSWER: ANSWER:

CorrectCorrect

± Resolving Vector Components with Trigonometry± Resolving Vector Components with Trigonometry

Often a Often a vectvector or is specifis specif ied bied by a magy a magnitude nitude and and a da direction; for irection; for example, a example, a roprope we with tension ith tension exerts a forexerts a force of ce of

magnitude magnitude in in a a diredirectction ion nornorth th of of east. east. This This is is a a good good way way to to think think of of vectvectors; ors; howhoweverever, , to to calculatecalculate

results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in thatresults with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that

coordinate system.coordinate system.

Part APart A

Find Find the the componecomponents nts of of the the vectvector or with with length length = = 1.00 1.00 and and angangle le =20.0 =20.0 with with respect respect to to thethe x x axis as shown axis as shown

in in ..

Enter numerically, separated by a comma, theEnter numerically, separated by a comma, the x x component followed by the component followed by the y y component. component.

, , == -2-2,-5 ,-5 ,,

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Hint 1.Hint 1. What is theWhat is the x x component? component?

Look at the figure shownLook at the figure shown

points in the positive points in the positive x x diredirectction, ion, so so isis

positivpositiv e. e. AlsAlso, o, the the magnitudmagnitude e is is just just thethe

length .length .

ANSWER: ANSWER:

CorrectCorrect

Part BPart B

Find Find the the componecomponents nts of of the the vectvector or with with length length = = 1.00 1.00 and and angle angle =20.0 =20.0 with with respect respect to to thethe x x axis as shown axis as shown

in in ..

Enter numerically, separated by a comma, theEnter numerically, separated by a comma, the x x component followed by the component followed by the y y component. component.

== 0.940,0.3420.940,0.342