Thursday, July 12, 2007

Irodov Problem 1.8

Let us suppose that the boats A and B each traveled a distance d from the buoy before turning back. Let the boats' speed be v and the river's speed be u.

For A while going downstream the river aided the boat, thus it moved with a speed v+u. On its upstream journey back to the buoy, however, the river was opposing the boat and so its speed was v-u. The total time taken by A thus is given by,

Similar to case of Swimmer 1 in Problem 1.7, for B to travel perpendicular to the buoy, he must move at an angle to the perpendicular. As in Problem 1.7 his speed perpendicular to the buoy is thus given by,. This will be the same B's return journey as well. Thus, the total time taken by him is given by,

Thus, from (1) and (2),

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