A 200-m wide river has a uniform flow speed of 1.1 m/s through a jungle and towa

Question

A 200-m wide river has a uniform flow speed of 1.1 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 4.0 m/s with respect to the water. There is a clearing on the north bank 82 m upstream from a point directly opposite the clearing on the south bank.

a.) In what direction 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

shortest distance = sqrt(290^2 + 18^2) = 290.55 290.55/sin90 = 96/sin(south) sin(south angle) = 0.33 south angle = 19.27 degrees north angle = 180 - 90 - 19.27 = 70.73 degrees 5/sin70.73 = .89/sinx sinx = 0.168 x = 9.67 a) Boat must be pointed at 9.67 degrees sqrt(.89^2 + 5.0^2) = 5.078 m/s 290.55 m / 5.078 m/s = 57.217 seconds b) IT TAKES 57.217 SECONDS TO CROSS

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