Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

Question

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Answer 1

Textbook Question

Chapter 2, Problem 2.1CYU

Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

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Answer 2

Textbook Question

Chapter 2, Problem 2.1CYU

Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

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Answer 3

Textbook Question

Chapter 2, Problem 2.1CYU

Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

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Answer 4

Textbook Question

Chapter 2, Problem 2.1CYU

Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

Answer 8

Expert Solution

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

Whether the given velocity vectors are equal or not.

Answer 13

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Answer 14

Explanation of Solution

Given:

Alice moves north at 6 knots and Bob moves west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6j^

The velocity vector for Bob is given by,

vBob=−6i^

Calculation:

Since the direction of the two vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 15

Expert Solution

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

(b)

Whether the given velocity vectors are equal or not.

Answer 20

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Answer 21

Explanation of Solution

Given:

Alice moves west at 6 knots and Bob moves west at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=−6i^

The velocity vector for Bob is given by,

vBob=−3i^

Calculation:

Since the magnitude of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 22

Expert Solution

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

(c)

Whether the given velocity vectors are equal or not.

Answer 27

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Answer 28

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south at 3 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=−3j^

Calculation:

Since the magnitude and the direction of the velocity vectors is different, the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 29

Expert Solution

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

(d)

Whether the given velocity vectors are equal or not.

Answer 34

Answer to Problem 2.1CYU

The given velocity vectors are not equal.

Answer 35

Explanation of Solution

Given:

Alice moves north east at 6 knots and Bob moves south west at 6 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=6cos(45°)i^+6sin(45°)j^=4.24i^+4.24j^

The velocity vector for Bob is given by,

vBob=6cos(225°)i^+6sin(225°)j^=−4.24i^−4.24j^

Calculation:

Since the magnitude of the vectors is same but the direction of the velocity vectors is different (antiparallel), the velocity vector of Alice is not equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are not equal.

Answer 36

Expert Solution

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

(e)

Whether the given velocity vectors are equal or not.

Answer 41

Answer to Problem 2.1CYU

The given velocity vectors are equal.

Answer 42

Explanation of Solution

Given:

Alice moves north east at 2 knots and Bob moves closer to shore north east at 2 knots.

Formula used:

The unit vector along the horizontal axis, that is the east direction is i^ and the unit vector along the vertical axis, that is north direction is j^.

The velocity vector for Alice is given by,

valice=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

The velocity vector for Bob is given by,

vBob=2cos(45°)i^+2sin(45°)j^=1.41i^+1.41j^

Calculation:

Since the magnitude as well as the direction of the velocity vectors is the same, the velocity vector of Alice is equal to the velocity vector of Bob.

Conclusion:

Therefore, the given velocity vectors are equal.