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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.
(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
Formula used:
The unit vector along the horizontal axis, that is the east direction is
The velocity vector for Alice is given by,
The velocity vector for Bob is given by,
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.
(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
Formula used:
The unit vector along the horizontal axis, that is the east direction is
The velocity vector for Alice is given by,
The velocity vector for Bob is given by,
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.
(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
Formula used:
The unit vector along the horizontal axis, that is the east direction is
The velocity vector for Alice is given by,
The velocity vector for Bob is given by,
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.
(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
Formula used:
The unit vector along the horizontal axis, that is the east direction is
The velocity vector for Alice is given by,
The velocity vector for Bob is given by,
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.
(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
Formula used:
The unit vector along the horizontal axis, that is the east direction is
The velocity vector for Alice is given by,
The velocity vector for Bob is given by,
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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Chapter 2 Solutions
University Physics Volume 1
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