InterviewSolution
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InterviewSolution
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A man wishes to row across a riverflowingto therightwith speed of 2m/s. If they velocity that the boat canhave V_(B) = 4 m//s , how should the man rowso as to reach across in . (a) shortest path (b)shortest time . |
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Answer» Solution :(a) Shortest Path . If the mainhasto move alongthe shortest path , then the path of thisboat should beAB ( perpepndicularto river). If THEMAN rows vertically , the riverwill carry him to right, hencethe MAN shouldinclinehis boat to theleft. Whenhis VELOCITYIS inclined ,it has two components , `V_(x)` and `V_(y)` [comparewith inclinedvelocity of cat].  Thehorizontal component `V_(x)` should cancel the SPEED the river . Thus`V_(x) = V_(B) cos theta = V_(R)` `therefore4 costheta=2 , theta = 60^(@)` Alternatively , we can use resultant vertical as in cat mouseproblem (Method 3). (b) Shortest time : Notethat whenthe man rows alongshortest distance , he DOES NOT cross the river in the shortest time , becausetime takento cross the river ` = ("widthe of river")/("vertical velocity")` As longas the boat is inclined at ANGLE `theta` , vertical velocityis `V_(B)`. To row in shortesttime ,theenitrevelocityof boatshould be used invertical direction i.e., Man shouldrowperpendicular to stream . Note: Whenthe man rows in shortest time , he does notreach pointB but instead point B. Shortest distanceis analogus to reachingapointon opposite bank(say house ) where shortest time is linked with onlyreachingopposite bank. 
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