Chapter 1

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Chapter 1

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Chapter 1 Due: 11:59pm on Sunday, January 20, 2019

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Exercise 1.10

Description: The following conversions occur frequently in physics and are very useful. (a) Use 1 (mi)=5280 (ft) and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 (ft)/s^2 . Use 1 (ft) = 30.48 (...

The following conversions occur frequently in physics and are very useful.

Part A Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. Express your answer using two significant figures. ANSWER:

88 f t/s

Part B

The

acceleration

of

a

freely

falling

object

is

32

2

f t/s

.

Use

1

ft

=

30.48

cm

to

express

this

acceleration

in

units

of

.2

m/s

Express your answer using two significant figures. ANSWER:

9.8

2

m/s

Part C

The

density

of

water

is

1.0

3

g/cm

.

Convert

this

density

to

units

of

.3

kg/m

Express your answer using two significant figures.

ANSWER:

1000

3

kg/m

Exercise 1.34

Description: (a) Find the magnitude of the vector A_1_vec represented by the pair of components A_x_1= A_x_1, A_y_1= A_y_1. (b) Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis...

Part A

Find the magnitude of the vector A1

represented by the pair of components Ax1

= -8.30 cm , Ay 1

= 1.90 cm .

ANSWER:



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= 8.51 cm

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Part B Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis. Find the direction of

the vector A1. ANSWER:

= 167

Part C

Find the magnitude of the vector A2 represented by the pair of components Ax2 = -5.50 m , Ay2 = -1.60 m . ANSWER:

= 5.73 m

Part D

Find the direction of the vector A2. Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis. ANSWER:

= 196

Part E

Find the magnitude of the vector A3

represented by the pair of components Ax3

= 7.40 km , Ay 3

= -3.60 km .

ANSWER:

= 8.23 km

Part F

Find the direction of the vector A3. Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis.

ANSWER:



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= 334

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Exercise 1.24

Description: (a) For the vectors A_vec and B_vec in the figure , use a scale drawing to find the magnitude of the vector sum A_vec+B_vec . (b) Find the direction of the vector sum A_vec+B_vec . (c) Find the magnitude of the vector difference A_vec - ...

Part A For the vectors A and B in the figure , use a scale drawing to find the magnitude of the vector sum A + B . Express your answer using two significant figures.

ANSWER: 9.0 m

Part B Find the direction of the vector sum A + B . Express your answer using two significant figures. ANSWER:

34 counterclockwise from +x-axis

Part C Find the magnitude of the vector difference A - B . Express your answer using two significant figures. ANSWER:

22 m

Part D

Find the direction of the vector difference A - B . Express your answer using three significant figures.

ANSWER:



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Part E

Use

your

answers

to

find

the

magnitude

of

-A

-

B .

Express your answer using two significant figures.

ANSWER:

9.0 m

Part F

Find

the

direction

of

-A

-

B .

Express your answer using three significant figures.

ANSWER:

214 counterclockwise from +x-axis

Part G

Find

the

magnitude

of

B

-

A

.

Express your answer using two significant figures.

ANSWER:

22 m

Part H

Find

the

direction

of

B

-

A

.

Express your answer using two significant figures.

ANSWER:

70 counterclockwise from +x-axis

Exercise 1.26

Description: A spelunker is surveying a cave. She follows a passage ## m straight west, then s2 in a direction 45 degree(s) east of south, and then 280 m at 30 degree(s) east of north. After a fourth unmeasured displacement, she finds herself back ...

A spelunker is surveying a cave. She follows a passage 170 m straight west, then 270 m in a direction 45 east of south, and then 280 m at 30 east of north. After a fourth unmeasured displacement, she finds herself back where she started.

Part A Use a scale drawing to determine the magnitude of the fourth displacement. Express your answer using two significant figures. ANSWER:



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MasteringPhysics: Print View with Answers = 170 m

Part B Determine the direction of the fourth displacement. Express your answer using two significant figures. ANSWER:

= 18 South of West

Exercise 1.38

Description: (a) Given the vector A_vec = 4.00 i_unit + 7.00 j_unit , find the magnitude of the vector. (b) Given the vector B_vec = 5.00 i_unit -2.00 j_unit , find the magnitude of the vector. (c) Write an expression for the vector difference...

Part A

Given

the

vector

A

=

4.00^i

+

7.00^j

,

find

the

magnitude

of

the

vector.

ANSWER:

8.06

Part B Given the vector B = 5.00^i - 2.00^j , find the magnitude of the vector. ANSWER:

5.39

Part C

Write

an

expression

for

the

vector

difference

A

-

B

using

unit

vectors.

Express your answer in terms of unit vectors.

ANSWER:

=

A-B

Part D

Find

the

magnitude

of

the

vector

difference

A

-

B .

ANSWER:



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Part E

Find

the

direction

of

the

vector

difference

A

-

B .

ANSWER:

96.3 counterclockwise from +x direction

Part F

In a vector diagram show A, B, and C = A - B . Draw the vectors starting at the black dot. Both the orientation and length of your vectors will be graded. Use "vector info" button to see the angle and length of your vectors. ANSWER:

No elements selected

Select the elements from the list and add them to the canvas setting the appropriate attributes.

Exercise 1.46

Description: (a) For the two vectors in the figure , find the magnitude of the vector product A_vec * B_vec. (b) Find the direction of the vector product A_vec * B_vec. (c) Find the magnitude of B_vec * A_vec. (d) Find the direction of B_vec * A_vec.



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Part A

For the two vectors in the figure , find the magnitude of the vector product A ? B .

ANSWER:

4.61

2

cm

Part B

Find

the

direction

of

the

vector

product

A

?

B .

ANSWER:

+z-direction -z-direction

Part C

Find

the

magnitude

of

B

?

A

.

ANSWER:

4.61

2

cm

Part D

Find

the

direction

of

B

?

A

.

ANSWER:

+z-direction -z-direction

Problem 1.66

Description: On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas . The directions are shown relative to north: 0 degree(s)is north, 90 degree(s)is east, 180 degree(s)is...

On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas . The

directions

are

shown

relative

to

north:

0

is

north,

90

is

east,

180

is

south,

and

270

is

west.



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Part A Use the method of components to find the distance she has to fly from Manhattan to get back to Lincoln. ANSWER: 189 km

Part B Find the direction (relative to north) she must fly to get there. ANSWER: = 350 Also accepted: -10.5

Problem 1.68

Description: An explorer in Antarctica leaves his shelter during a whiteout. He takes n1 steps northeast, then n2 steps at an angle 60 degree(s) north of west, then n3 steps due south. Assume his steps all have equal length. (a) Select the... An explorer in Antarctica leaves his shelter during a whiteout. He takes 39 steps northeast, then 82 steps at an angle 60 north of west, then 49 steps due south. Assume his steps all have equal length.

Part A Select the correct diagram, roughly to scale, of the three vectors and their resultant. ANSWER:



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