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`        An aeroplane fly  along a straight path AB and return back again, the distance between A and B is L. The aeroplane maintains the consrant speed V w.r.t wind, there is a steady wind with speed U and at  angle ‘theta’ with line AB. Then calculate total time of the trip.`
4 months ago

Vikas TU
9455 Points
```							Hiii Speed of wind = UHorizontal component of U will oppse the aeroplane in travelling from A to B.Speed while going from A to B = V – U cosQSpeed while coming from Bto A = V + U cosQTotal time = L(1/(V – U cosQ) + 1/V + U cosQ))Hope this helps.
```
4 months ago
Khimraj
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 is1/ V +vAnd the time in the upwind half is1/ V-vSo, 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^2Combining like terms,2 V / V^2 -v^2If V = 1, and v = .1, when AB = 1,2 / 1 - .012 / .99Total time is 2.02 unitsTo put this into a real-world scenario:Instead of AB being 1,AB= 100 milesV=100 mphv=10 mphDownwind time: 100/110Upwind time: 100/90Total time: (100/110) + (100/90)(9000/9900) + (11000/9900)20,000/9900Total time is 2.02 hoursThis is not the 2.00 hours found by doubling the distance and assuming the winds cancel out.
```
4 months ago
aswanth nayak
68 Points
```							Dear Student,   Does “AB=1” mean “the distance from A to B is 1?”If so, the time (distance divided by speed) in the downwind half is1/ V +vAnd the time in the upwind half is1/ V-vSo, 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^2Combining like terms,2 V / V^2 -v^2If V = 1, and v = .1, when AB = 1,2 / 1 - .012 / .99Total time is 2.02 unitsTo put this into a real-world scenario:Instead of AB being 1,AB= 100 milesV=100 mphv=10 mphDownwind time: 100/110Upwind time: 100/90Total time: (100/110) + (100/90)(9000/9900) + (11000/9900)20,000/9900Total time is 2.02 hoursThis is not the 2.00 hours found by doubling the distance and assuming the winds cancel out.  Hope this helps you  regards
```
3 months ago
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• 110 Video Lectures
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• Test paper with Video Solution
• Mind Map
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• NCERT Solutions
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