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Grade: 11
an aeroplane fly along a straight path AB and return back again. The distance between A and B is l, and the aeroplane maintain the constant speed v w.r.t wind.There is a steady wind with  speed u and at angle ‘theta” with the line AB. Then calculate total time if the trip.
2 months ago

Answers : (2)

Vikas TU
8729 Points
Just check ,i have answered the same question earlier , you just need to find the horizonta component of wind, which will be in relative velocity to the aeroplane traveled , and , take the relative velocity in coming nd going , and find the time accordingly and at last add both of them.
2 months ago
3008 Points

Does “AB=1” mean “the distance from A to B is 1?”

If so, the time (distance divided by speed) in the downwind half is

1/ V +v

And the time in the upwind half is

1/ V-v

So, the total time is (1/V+v) + (1/V-v)

Working toward a common denominator,

{(V-v) + (V+v)} / (V-v) (V+v)


2 V / V^2 + V v - V v -v^2

Combining like terms,

2 V / V^2 -v^2

If V = 1, and v = .1, when AB = 1,

2 / 1 - .01

2 / .99

Total time is 2.02 units

To put this into a real-world scenario:

Instead of AB being 1,

AB= 100 miles

V=100 mph

v=10 mph

Downwind time: 100/110

Upwind time: 100/90

Total time: (100/110) + (100/90)

(9000/9900) + (11000/9900)


Total time is 2.02 hours

This is not the 2.00 hours found by doubling the distance and assuming the winds cancel out.

2 months ago
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