French, asked by ayushyele, 11 months ago

An aeroplane has to go along straight line from A to B, and back again. The relative speed with respect
to wind is V. The wind blows perpendicular to line AB with speed v. The distance between A and B is l.
The total time for the round trip is :​

Answers

Answered by Anonymous
18

Answer:

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)

Then,

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)

20,000/9900

Total time is 2.02 hours

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

Answered by kanchisingh66
2

Answer:

From the relative velocity concept:

when going from A to B time taken=>

t1 = l/(V-v)

from B to A while returning,

t2 = l /(V+v)

Total Time = t1 + t2 => l /(V+v) + l /(V-v) = > l/(1/(V-v) + 1/(V+v)) seconds.

Hope it's help you.....

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