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A pilot is supposed to fly due east from A to B and then back again to A due west. The velocity of the plane in air is and the velocity of the air with respect to the ground is . The distance between A and B is I and the plane's air speed is constant. (a)If u = 0 (still air), show that the time for the round trip is to = 21/v. (b) Suppose that the air velocity is due east (or west). Show that the time for a round trip is then (c) Suppose that the air velocity is due north (or south). Show that the time for a round trip is then (d) In parts (b) and (c) one must assume that II

A pilot is supposed to fly due east from A to B and then back again to A due west. The velocity of the plane in air is and the velocity of the air with respect to the ground is . The distance between A and B is I and the plane's air speed is constant. (a)If u = 0 (still air), show that the time for the round trip is to = 21/v. (b) Suppose that the air velocity is due east (or west). Show that the time for a round trip is then
(c) Suppose that the air velocity is due north (or south). Show that the time for a round trip is then
(d) In parts (b) and (c) one must assume that II

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
234-572_1.PNG
(b)
When the plane moves east, the net velocity of the plane in air is:
234-138_1.PNG
Now, the time to reach its destination is:
234-2210_1.PNG
When the plane moves west, the net velocity of the plane in air is:
234-72_1.PNG
Now, the time to reach its destination is:
234-1727_1.PNG
The total time taken by the plane to complete the trip is:
234-466_1.PNG
234-807_1.PNG
(c)
The speed of the plane in air, when the air moves North or South is:

234-51_1.PNG
The speed of the plane remains the same on its round trip, and therefore the total time taken by the plane is:
234-2473_1.PNG
234-1072_1.PNG
(d)
It is important to note that in parts (b) and (c) one must assume that v > u or else the time t will be negative and imaginary correspondingly. Therefore, the plane may get to its destination in one direction, but it cannot fly back in real time.

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