Concept explainers
An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north, (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 km/h to the east relative to the ground?
(a)
The time interval for the trip if the plane flies trough a headwind blowing at
Answer to Problem 26P
The time interval for the trip is
Explanation of Solution
Let positive
The displacement of the plane relative to the ground is,
The displacement of the plane relative to the air is,
The displacement of the air relative to the ground is,
From the vector triangle, equating the
Here,
Substitute
Equating the
Substitute
The wind blows towards south (
Substituting
Conclusion:
Thus, the time interval for the trip is
(b)
The time interval for the trip if the plane flies trough a tailwind blowing at
Answer to Problem 26P
The time interval for the trip is
Explanation of Solution
We have the second equation,
As the wind blows northward as a tailwind, substitute
Conclusion:
The time interval for the trip is
(c)
The time interval for the trip if the plane flies trough a crosswind blowing at
Answer to Problem 26P
The time interval for the trip is
Explanation of Solution
We have the first equation,
As the wind blows east, substitute
That is, the plane must fly
We have the second equation,
Substitute
Conclusion:
Thus, the time interval for the trip is
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