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Anonymous asked in Science & MathematicsPhysics · 1 month ago

# (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?

Relevance
• 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)

and so

V = 2s * √[(t1+t2) / t1*(t1*t2)]

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