An aeroplane has to go along straight line from A to B, and back again

1.	An aeroplane has to go along straight line from A to B, and back again. The relative speed with respectto 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 :
Answer» 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.

An aeroplane has to go along straight line from A to B, and back again. The relative speed with respectto 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 :

Answer»

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.