Find the time an aeroplane having velocity `v` takes to fly around a square with side `a` if the wind is blowing at a velocity `u` along one side of the square.\

Explanation

Velocity of aeroplane while flying through `AB`,
`v_A = v + u`
`t_(A B) = (a)/(v + u)`
Velocity of aeroplane while flying through `BC`,
`v_A = sqrt(v^2 - u^2)`
`t_(BC) = (a)/(sqrt(v^2 - u^2))`
Velocity of aeroplane while flying through `CD`
`v_A = v - u`
`t_(CD) = (a)/(v - u)`
Velocity of aeroplane while flying through `D A`,
`v_A = sqrt(v^2 - u^2)`
`t_(DA) = (a)/(sqrt(v^2 - u^2)`
Total time `= t_(AB) + t_(BC) + t_(CD) + t_(DA)`
=`(a)/(v + u) + (a)/(sqrt(v^2 - u^2) + (a)/(v - u) + (a)/(sqrt(v^2 - u^2))`
=`(2 a)/(v^2 - u^2) (v + sqrt(v^2 - u^2))`.
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