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June 9th, 2018, 09:33 PM  #1 
Member Joined: Jul 2017 From: KOLKATA Posts: 33 Thanks: 2  Relative velocity
While a boat cruises down a river, it crosses a wooden log at a particular point of time. Then the boat travels along the river for a time C and reverses its direction to travel upstream for a time T, when it meets the same wooden log, which has been freely drifting along the river all the while. If the engine of the boat has been working at the same power level throughout its journey, express T in terms of C. My answer came out: T = C. Could anyone please confirm as the answer given is roman Tau. Last edited by skipjack; June 10th, 2018 at 02:09 AM. 
June 9th, 2018, 09:54 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,382 Thanks: 1281 
Let the boat meet the log the first time at $t=0$ Also let the boat's velocity in still water be $v_b$ The log drifts at the velocity of the current $v_c$ $C(v_b + v_c) + T(v_cv_b) = v_c (C+T)$ This does simplify to $T=C$ 
June 9th, 2018, 10:02 PM  #3 
Member Joined: Jul 2017 From: KOLKATA Posts: 33 Thanks: 2 
Many Thanks . I got confused with the answer given in the book.


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