A 140-m-wide river has a uniform flow speed of 0.54 m/s through a jungle and tow

Question

A 140-m-wide river has a uniform flow speed of 0.54 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 6.6 m/s with respect to the water. There is a clearing on the north bank 83 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?

Explanation / Answer

a) so make up and down stream x and across y

then if leaving at an angle from flow

x = (6.6*cos(theta) - 0.54)t=83

y = 6.6 sin (theta) t = 140

t = 140/(6.6 sin(theta))

(6.6 cos(theta) - 0.54) *140/(6.6*sin(theta)) = 83

theta = 55.3 degrees

b)

so t = 140/(6.6*sin(55.3 degrees))=25.8 s

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