A river 500 ft wide flows with a speed of 8 ft/s with respect to the earth. A wo

Question

A river 500 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.

1)If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?
d1 =

2)If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight accross, as in part (a)), how far downstream is she swept before reaching the opposite bank?
d2 =

3)For the conditions of part (b), how long does it take for her to reach the opposite bank?
t =

Explanation / Answer

1) time to reach other side = 500/4 = 125 s distance traveled in this time downstream = 8*125 = 1000 ft 2) velocity component across the river = 4cos(37) time to reach other side = 500/4cos(37) = 156.52 s distance traveled in this time downstream = (8-4sin(37))*156.52 = 875.38 ft 3) time to reach other side t= 500/4cos(37) = 156.52 s

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