(Physics question) City A lies directly west of city B. ... How fast is the wind blowing?
City A lies directly west of city B. When there is no wind, an airliner makes the round trip flight of distance s between them in a flight time of t1 while traveling at the same speed in both directions. When a strong, steady wind is blowing from west to east and the airliner has the same air speed as before, the round trip takes a flight time of t2
How fast is the wind blowing?
- NCSLv 74 weeks ago
speed with no wind is
v = 2s / t1
With a wind of speed V parallel to the direction of travel, the time with the wind is
t' = s / (v+V)
and the time against the wind is
t" = s / (v - V)
for total time of
t2 = t' + t" = s/(v+V) + s/(v-V) = s*[1/(v+V) + 1/(v-V)]
t2 = s*[(v-V) + (v+V)] / (v+V)(v-V)
t2 = s*[2v] / (v² - V²)
v² - V² = 2*s*v / t2
V² = v² - 2*s*v / t2
let's substitute v = 2s / t1
V² = (2s/t1)² - 2s(2s/t1)/t2 = (4s²/t1)(1/t1 - 1/t2) = 4s² * (t2-t1) / t1*(t1*t2)
V = 2s * √[(t1+t2) / t1*(t1*t2)]
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- Larry K.Lv 71 month ago
It doesn't matter how fast the wind is blowing. the flight time will be T1. the reason is that whatever the wind speed, it will add to the speed in one half of the trip going towards the city and subtract from the speed going the other way. So if we make the time when blowing with the airplane's speed T1 - T2 and T1 + T2 when subtracting from the airplane's speed, the total average time of the plane over the entire trip will be (T1 + T2 + T1 - T2)/2 = T1
Andy, this is the answer. It's T1 (the same as when there's no wind at all).