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In a river flowing at 20 m//s, a swimmer...

In a river flowing at `20 m//s`, a swimmer who can swin at `10 m//s` relative to water jumps from on bank of the river. The direction from normal to the bank of river at which swimmer should swim so as to minimize the drifts is `(pi)/(x)` rad. Then x is

Text Solution

Verified by Experts

The correct Answer is:
6

`t = (d)/(v cos theta)`
`s = "drift" = (u - v sin theta) (d)/(v) cos theta` to minimize `s, (ds)/(d theta) = 0`
`rArr s = (u d sec theta)/(v) - d tan theta`
`(ds)/(d theta) = (4d)/(v) sec theta tan theta - d sec^(2) theta = 0`
`sec theta = 0` or `(4d)/(v) tan theta = d sec theta`
`(u)/(v) (sin theta)/(cos theta) = (1)/(cos theta)`
`sin theta = (v)/(u)`
`theta = sin^(-1) ((v)/(u))`
`theta = sin^(-1) ((10)/(20)) = sin^(-1) ((1)/(2))`
`theta = 30^(@) = (pi)/(6)`
`x = 6`
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