Thursday, July 12, 2007

Irodov Problem 1.7

Let us call the swimmer who swam directly from A to B as S1 and the other swimmer as S2.

S1, in-order to swim directly to B from A, had to oppose the flow of the river and completely annul it. This means that S1 must have had to swim at an angle from the line AB such that, the velocity component along the direction of river flow must be exactly equal and opposite to that of the river flow.
Thus we have,
Swimmer S1's component along the direction AB is then given by,




If the length if AB is d then the time taken by swimmer S1 to reach B is given by,








Swimmer S2 however, swims perpendicular to the river's flow and hence will be swept off to the right by the river. His speed in the direction perpendicular to the river will be v' and the river will push him to the right with a speed vo. Thus, swimmer S2 will take time to reach the other shore at point C as seen in the figure. Since, he has been drifting to the right with a speed v' to the right, BC will be equal to . He will thus take time to reach B from C. This means that the total time swimmer S2 takes to reach B via C will be equal to,



Since both the swimmers reach at the same time, we have,

5 comments:

Anonymous said...

Why is it assumed that swimmer S2 swims perpendicular to the stream? He might as well have a velocity component along or opposite to the direction of river stream. In other words, why is it assumed that only river drift will contribute to the motion of S2 along the flow of the river? Can somebody give me a satisfactory answer, please?

Anonymous said...

thats correct

Anonymous said...

I agree

Anonymous said...

Thank You!

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