TACTICS BOX 3.3 Determining the components of a vector

10/6/2014 HW3

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HW3 Due: 11:59pm on Monday, October 13, 2014

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Tactics Box 3.3 Determining the Components of a Vector

Learning Goal:

To practice Tactics Box 3.3 Determining the component of a vector.

When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This Tactics Box describes how to determine the x component and y component of vector , denoted and .

TACTICS BOX 3.3 Determining the components of a vector

1. The absolute value of the x component is the magnitude of the component vector .

2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction.

3. The y component is determined similarly.

Part A

What is the magnitude of the component vector shown in the figure?

Express your answer in meters to two significant figures.

ANSWER:

Part B

What is the sign of the y component of vector shown in the figure?

A ⃗ A ⃗ x A ⃗ y

A ⃗ Ax Ay

| |Ax Ax A ⃗ x

Ax A ⃗ x A

⃗ x

Ay

A ⃗ x

= | |Ax m

Ay A ⃗

10/6/2014 HW3

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ANSWER:

Part C

This question will be shown after you complete previous question(s).

Components of Vectors

Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified.

Part A

What is the x component of ?

Express your answer to two significant figures.

positive negative

A ⃗ D⃗

A ⃗

10/6/2014 HW3

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You did not open hints for this part.

ANSWER:

Part B

What is the y component of ?

Express your answer to the nearest integer.

ANSWER:

Part C

What is the y component of ?

Express your answer to the nearest integer.

You did not open hints for this part.

ANSWER:

Part D

What is the component of ?

Express your answer to the nearest integer.

You did not open hints for this part.

ANSWER:

The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation.

The answers below are all integers, so estimate the components to the nearest whole number.

= Ax

A ⃗

= Ay

B⃗

= By

x C ⃗

= Cx

A ⃗

10/6/2014 HW3

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Part E

In ordered pair notation, write down the components of vector .

Express your answers to the nearest integer.

ANSWER:

Part F

In ordered pair notation, write down the components of vector .

Express your answers to the nearest integer.

ANSWER:

Part G

What is true about and ? Choose from the pulldown list below.

ANSWER:

Problem 3.15

A wildlife researcher is tracking a flock of geese. The geese fly 4.5 due west, then turn toward the north by 50 and fly another 5.0 .

Part A

How far west are they of their initial position?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Part B

B⃗

, = Bx By

D⃗

, = Dx Dy

B⃗ D⃗

They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.

km ∘ km

= dw

10/6/2014 HW3

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What is the magnitude of their displacement?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Problem 3.5

A position vector with magnitude 20 points to the right and up. Its -component is 16 .

Part A

What is the value of its -component?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Problem 3.2

Part A

Draw the vector .

ANSWER:

= d

m x m

y

= y

= +C ⃗ A ⃗ B⃗

10/6/2014 HW3

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Part B

Draw the vector .

ANSWER:

= −D⃗ A ⃗ B⃗

10/6/2014 HW3

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Problem 3.1

Part A

Draw the vector .

ANSWER:

Part B

Draw the vector .

ANSWER:

= +D⃗ A ⃗ B⃗

= −C ⃗ A ⃗ B⃗

10/6/2014 HW3

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Vector Magnitude and Direction Conceptual Question

A man out walking his dog makes one complete pass around a perfectly square city block. He starts at point A and walks clockwise around the block.

Let be the displacement vector from A to B, be the displacement vector from B to C, etc.

Part A

Which of the following vectors is equal to ?

You did not open hints for this part.

r ⃗ AB r ⃗ BC

r ⃗ AB

10/6/2014 HW3

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ANSWER:

Part B

Which of the following vectors is equal to ?

ANSWER:

Part C

Which of the following vectors is equal to ?

You did not open hints for this part.

ANSWER:

Adding and Subtracting Vectors Conceptual Question

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

only

only

only All of the above None of the above

r ⃗ BC r ⃗ CD r ⃗ DA

−r ⃗ AB

only

only

only All of the above None of the above

r ⃗ BC r ⃗ CD r ⃗ DA

−r ⃗ AB r ⃗ DA

only

only

only All of the above None of the above

−( + )r ⃗ CD r ⃗ DA +r ⃗ AB r ⃗ BC −r ⃗ BC r ⃗ CD

10/6/2014 HW3

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Part A

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

You did not open hints for this part.

ANSWER:

Part B

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

You did not open hints for this part.

ANSWER:

Part C

C and E E and F A and F C and D B and D

C and D A and F E and F A and B E and D

10/6/2014 HW3

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

You did not open hints for this part.

ANSWER:

Vector Addition Ranking Task

Six vectors ( through ) have the magnitudes and directions indicated in the figure.

Part A

Rank the vector combinations on the basis of their magnitude.

Rank from largest to smallest. To rank items as equivalent, overlap them.

You did not open hints for this part.

ANSWER:

A and F A and E D and B C and D E and F

a ⃗ f ⃗

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Part B

Rank the vector combinations on the basis of their angle, measured counterclockwise from the positive x axis. Vectors parallel to the positive x axis have an angle of 0 . All angle measures fall between 0 and 360 .

Rank from largest to smallest. To rank items as equivalent, overlap them.

You did not open hints for this part.

ANSWER:

∘ ∘ ∘

10/6/2014 HW3

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Adding Scalar Multiples of Vectors Graphically

Draw the vectors indicated. You may use any extra (unlabeled) vectors that are helpful; but, keep in mind that the unlabeled vectors should be deleted before submitting your answer.

Part A

Draw the vector .

The length and orientation of the vector will be graded. The location of the vector is not important.

You did not open hints for this part.

ANSWER:

= + 2C ⃗ A ⃗ B⃗

10/6/2014 HW3

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Part B

Draw the vector .

The length and orientation of the vector will be graded. The location of the vector is not important.

You did not open hints for this part.

ANSWER:

= 1.5 − 3C ⃗ A ⃗ B⃗

10/6/2014 HW3

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Part C

Draw the vector .

The length and orientation of the vector will be graded. The location of the vector is not important.

You did not open hints for this part.

ANSWER:

= 0.5 + 2C ⃗ A ⃗ B⃗

10/6/2014 HW3

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Tactics Box 3.1 Subtracting Vectors

Learning Goal:

To practice Tactics Box 3.1 Subtracting vectors

Vector subtraction has some similarities to the subtraction of two scalar quantities. With numbers, subtraction is the same as the addition of a negative number. For example, is the same as . Similarly,

. We can use the rules for vector addition and the fact that is a vector opposite in direction to to form rules for vector subtraction, as explained in this Tactics Box.

TACTICS BOX 3.1 Subtracting vectors

To subtract from perform these steps:

1. Draw .

2. Place the tail of at the tip of .

5 − 3 5 + (−3) − = + (− )A ⃗ B⃗ A ⃗ B⃗ −B⃗

B⃗

B⃗ A ⃗

A ⃗

−B⃗ A ⃗

10/6/2014 HW3

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3. Draw an arrow from the tail of to the tip of . This is vector .

Part A

Find vector by following the steps in the Tactics Box above. Make certain to draw with the correct orientation.

ANSWER:

Part B

Find vector by following the steps in the Tactics Box above. Make certain to draw with the correct orientation.

ANSWER:

A ⃗ −B⃗ −A ⃗ B⃗

= −C ⃗ A ⃗ B⃗ −B⃗

= −F ⃗ D⃗ E ⃗ −E ⃗

10/6/2014 HW3

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± Resolving Vector Components with Trigonometry

Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system.

Part A

Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown.

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

You did not open hints for this part.

T ⃗ T ∘

A ⃗ a α ∘

10/6/2014 HW3

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ANSWER:

Part B

Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown.

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

You did not open hints for this part.

ANSWER:

Part C

Find the components of the vector with length = 1.00 and angle 35.0 as shown.

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

You did not open hints for this part.

ANSWER:

± Biking Vectors

A student bikes to school by traveling first = 1.00 north, then = 0.500 west, and finally = 0.100 south.

Part A

If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance would the bird cover?

Express your answer in miles.

You did not open hints for this part.

ANSWER:

= A ⃗

B⃗ b β ∘

= B⃗

C ⃗ c ϕ = ∘

= C ⃗

dN miles dW miles dS miles

db

10/6/2014 HW3

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Part B

This question will be shown after you complete previous question(s).

Part C

This question will be shown after you complete previous question(s).

Part D

This question will be shown after you complete previous question(s).

Part E

This question will be shown after you complete previous question(s).

Part F

This question will be shown after you complete previous question(s).

Problem 3.8

Josh is climbing up a steep 32 slope, moving at a steady 0.90 along the ground in .

= db miles

∘ m/s

10/6/2014 HW3

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Part A

How many meters of elevation does he gain in one minute of this climb?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 105 points.

= d

 

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