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A person rows a boat across a river maki...

A person rows a boat across a river making an anglen of `60^@` with the downstream. Find the percentage time he would have saved, ahd he crossed the river in the shortest possible time.

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Let `v` be the velocity of the boat and `d` the width of the river. The component of velocity along the direction perpendicular to the flow of water current is `v sin 60^@`. Now, if `f_1` be the time taken by the person to cross the river, then
`t_1 = (d)/(v sin 60^@) = (d)/(v) ((2)/(sqrt(3)))`
Had he crossed the river in the minimum possible time, then his direction should always be perpendicular to the flow of river and the corresponding time taken,
`t_2 (say) = (d)/(v)`
`:.` Percentage time saved =`(t_1 - t_2)/(t_2) xx 100`
=`((d)/(v)((2)/(sqrt(3)))- (d)/(v))/(d/v) xx 100 = 15.47 %`.
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