A woman who can row a boat at 5.1 km/h in still water faces a long, straight riv

Question

A woman who can row a boat at 5.1 km/h in still water faces a long, straight river with a width of 6.4 km and a current of 3.5 km/h. Let i point directly across the river and j point directly downstream. If she rows in a straight line to a point directly opposite her starting position, (a) at what angle to i must she point the boat and (b) how long (in hours) will she take? (c) How long (in hours) will she take if, instead, she rows 3.8 km down the river and then back to her starting point? (d) How long (in hours) if she rows 3.8 km up the river and then back to her starting point? (e) At what angle to i should she point the boat if she wants to cross the river in the shortest possible time? (f) How long (in hours) is that shortest time?

Explanation / Answer

(a) Angle = sin^-1(3.5/5.1) = 43.33 degrees from i away from j. (b) speed towards i = sqrt(5.1^2 -3.5^2) = 3.71 m/s Time taken = 6.4/3.71 = 1.725 hours (c) 3.8/(5.1+3.5) + 3.8/(5.1-3.5) = 2.817 hours (d) 3.8/(5.1-3.5) + 3.8/(5.1+3.5) = 2.817 hours (e) She should point the boat towards i. (f) t = 6.4/5.1 = 1.25 hours

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