Adding scalar multiples of vectors graphically mastering physics

10/6/2014 HW3

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 1/21

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

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 9/21

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