Concept explainers
(a)
The displacement of the plane from its starting point.
(a)
Answer to Problem 81P
The person S’s speed with respect to the starting point on the bank is
Explanation of Solution
The person S’s motion is shown in Figure 1.
Write an expression to calculate the x component of the speed of person S with respect to the starting point on the bank.
Here,
Write an expression to calculate the y component of the speed of the person S.
Here,
Write an expression to calculate the speed of the person with respect to the starting point on the bank.
Conclusion:
Substitute
Substitute
Substitute
Thus, the person S’s speed with respect to the starting point on the bank is
(b)
The direction at which the jetliner have flown directly to the same destination.
(b)
Answer to Problem 81P
The time taken to cross the river is
Explanation of Solution
Write an expression to calculate the time taken to cross the river.
Here,
Conclusion:
Substitute
Thus, the time taken to cross the river is
(c)
The time taken for the trip.
(c)
Answer to Problem 81P
The upstream or downstream of the person S from the starting point the person S reaches at the opposite bank is
Explanation of Solution
Write an expression to calculate the upstream or downstream of the person S from the starting point the person S reaches at the opposite bank.
Here,
Conclusion:
Substitute
Thus, the upstream or downstream of the person S from the starting point the person S reaches at the opposite bank is
(d)
The time taken for the direct flight.
(d)
Answer to Problem 81P
The upstream angle the person S should go in order to go straight across is
Explanation of Solution
The upstream component of her velocity relative to the water should be equal in magnitude to the velocity of the current relative to the bank.
Write an expression to calculate the launch angle
Here,
Rearrange the equation (VI) to find
Conclusion:
Substitute
Thus, the upstream angle the person S should go in order to go straight across is
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