A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s. a. What is the length of the arrow that Clarisse draws? b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale? c. Is one student’s choice better than the other? If so, what makes it a better scale?

Question

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Answer 1

Textbook Question

Chapter 3, Problem 1PQ

A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s.

a. What is the length of the arrow that Clarisse draws?

b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale?

c. Is one student’s choice better than the other? If so, what makes it a better scale?

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

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Answer 2

Textbook Question

Chapter 3, Problem 1PQ

A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s.

a. What is the length of the arrow that Clarisse draws?

b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale?

c. Is one student’s choice better than the other? If so, what makes it a better scale?

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

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Answer 3

Textbook Question

Chapter 3, Problem 1PQ

A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s.

a. What is the length of the arrow that Clarisse draws?

b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale?

c. Is one student’s choice better than the other? If so, what makes it a better scale?

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

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Answer 4

Textbook Question

Chapter 3, Problem 1PQ

A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s.

a. What is the length of the arrow that Clarisse draws?

b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale?

c. Is one student’s choice better than the other? If so, what makes it a better scale?

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

Answer 8

(a)

Expert Solution

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The length of the arrow drawn to represent velocity vector using Clarisse’s scale.

Answer 13

Answer to Problem 1PQ

The length of the arrow is 7.20 cm.

Answer 14

Explanation of Solution

The magnitude of the velocity vector is 720 ms−1. In Clarisse’s scale 1 cm→100 ms−1.

When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be 720 ms−1.

Represent the length in Clarisse’s scale

720 ms−1→720 ms−1⋅1 cm100 ms−1→7.20 cm

Conclusion:

Thus, the length of the arrow is 7.20 cm.

Answer 15

(b)

Expert Solution

To determine

The scaling chosen by Francois’s scale.

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The scaling chosen by Francois’s scale.

Answer 20

Answer to Problem 1PQ

In Francois’s scale, 1 cm→200 ms−1.

Answer 21

Explanation of Solution

The length of Francois’s arrow is half of the length of Clarisse’s scale i.e. 7.20 cm2=3.60 cm. This length represents the magnitude of the vector i.e. 3.60 cm→720 ms−1.

Divide on both sides by 3.60

1 cm→720 ms−13.60→200 ms−1

Thus, in Francois’s scale, 1 cm→200 ms−1.

Answer 22

(c)

Expert Solution

To determine

Explain whether one scale choice is better than the other.

Answer to Problem 1PQ

No, either of the scales can be used.

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Explain whether one scale choice is better than the other.

Answer 27

Answer to Problem 1PQ

No, either of the scales can be used.

Answer 28

Explanation of Solution

Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.

Conclusion:

No, either of the scales can be used.