A man crosses a river by a boat. If he crosses the river in minimum time he take 10 minutes with a drift 120m. If he crosses the river taking shortest path, he takes 12.5 minutes. Assuming `v_(b//r) gt v_(r)`, find (i) width of the river, (ii) velocity of the boat with respect to water `(v_(b//r))` (iii) speed of the current `(v_(r))`

Answer

`200 m, v_("boat")=1.20 km//hr, v_("water")=0.72 km//hr`,

Explanation

`t=d/v_(B)=600s," drift"=v_(w)xxd/v_(B)`
`120=" "v_(w)xx600s, v_(w)=1/5m/(sec)`
`t=(d)/sqrt(v_(B)^(2)-v_(w)^(2))=750`
`sqrt(1-(v_(w)/v_(B))^(2))=4/5 rArr (v_(w)/v_(B))^(2)=9/25`
`v_(w)/v_(B)=3/5rArr v_(B)=(1//5)/(3//5)=1/3 m//sec`
`d/V_(B)=600=d=600xx1/3=200 m`