A stream that is flowing from the north to the south at 1.5 m/s is 30 meters wide. If a boat launched from the east shore is traveling 2 m/s west with respect to the shore. How long does it take to cross the river? 

Expert Answers

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The width of the stream = 30 m

Stream velocity (from north to south) = 1.5 m/s

Boat velocity (from east to west) =  2 m/s

Time required to cross the stream = distance/boat velocity = 30 m/ 2 m/s = 15 sec.

Thus, it would take 15 sec for the boat to cross the stream.

Interestingly, many students would be tempted to use the average velocity of boat, which would be a resultant of the boat velocity and stream velocity. This average flow velocity can be determined by Pythagoras Theorem (as the square root of sum of the squares of stream velocity and boat velocity). However, the average flow velocity will take the boat in South-West direction, with respect to the starting point at the shore. And hence, we must use the actual path traveled and not the width of stream, if we are using average flow velocity.

Hope this helps.  

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