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The velocity of water current in a river...

The velocity of water current in a river changes with distance along the perpendicular to the river according to the law `u=(2u_(0))/(d)y " for " 0 le y le (d)/(2)` where `u_(0)`= velocity in the mid-stream d= width of the river `=(2 u_(0))/(d)(d-y) " for " (d)/(2) le y le d`.
A boat travels from a point O on one block of the river to the opposite bank and its steering angle is constantly changed to keep its relative velocity perpendicular to the river current. Calculate the time in which the boat will reach the other bank. The velocity of the boat in still water is `u_(0)`.

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The correct Answer is:
`(pi d)/(2 u_(0))`
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