A woman who can row a boat at 5.10 km/h in still water faces a long, straight ri

Question

A woman who can row a boat at 5.10 km/h in still water faces a long, straight river with a width of 5.10 km and a current of 3.50 km/h. Let , point directly across the river and point directly downstream. If she rows in a straight line to a point directly opposite her starting position, (a) at what angle to must she point the boat and (b) how long will she take? (c) How long will she take if, instead, she rows 3.50 km down the river and then back to her starting point? (d) How long if she rows 3.50 km up the river and then back to her starting point? (e) At what angle to' should she point the boat if she wants to cross the river in the shortest possible time? (f) How long is that shortest time?

Explanation / Answer

(a) She must "build" an upstream (negative in this reference frame) component into her velocity:
= arctan(-3.5/5.1) = -34.46º (that is, 34.46º "upstream")

(b) t = d / v = 5.1km / (5.1km/h*cos34.46º) = 0.825 h = 49.47 min

(c) downstream: t_d = d / v = 3.5km / (5.1+ 3.5)km/h
t_d = 0.41 h = 24.42 min
upstream: t_d = 3.5km / (5.1 - 3.5)km/h = 2.1875 h = 131.25 min
total time t = 155.67 min

(d) same total time

(e) If "cross the river" means "reach any point on the other shore," then she should aim straight across: = 0º.

(f) t = 5.1km / 5.1km/h = 60 min

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