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A man crosses a river in a boat. If he c...

A man crosses a river in a boat. If he cross the river in minimum time he takes `10 min` with a drift `120 m.` If he crosses the river taking shortest path, he takes `12.5 min,` find
(a) width of the river
(b) velocity of the boat with respect to water
(c) speed of the current

Text Solution

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The correct Answer is:
`200 m, v_("boat")=1.20 km//hr, v_("water")=0.72 km//hr`,

`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`
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