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.
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.
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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2. A projectile is shot from a launcher at an angle 0,, with an initial velocity
magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a
child's noggin (see Figure 1). The apple is a height y above the tabletop, and a
horizontal distance x from the launcher. Set this up as a formal problem, and solve
for x. That is, determine an expression for x in terms of only v₁, 0, y and g.
Actually, this is quite a long expression. So, if you want, you can determine an
expression for x in terms of v., 0., and time t, and determine another expression for
timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of
t into the expression for x. Your final equation(s) will be called Equation 3 (and
Equation 4).
Draw a phase portrait for an oscillating, damped spring.
A person is running a temperature of 41.0°C. What is the equivalent temperature on the Fahrenheit scale? (Enter your answer to at least three significant figures.)
°F
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