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Question

You wish to row straight across a 80-m-wide river. You can row at a steady 1.6 m/s relative to the water, and the river flows at 0.44 m/s.

a) in what direction should you head? angle= ??? degrees (measured from direction of current)

b) How long will it take to cross the river? time= ??? seconds

Answer 1

a)

First of all the speed of the boat with respect to the ground is

v = 1.6 m/s + .44 m/s = 2.04 m/s

In order for the boat to go straight across, the component of the boat's velocity parallel to the river must be equal and opposite the river's velocity.

v(parallel) = .44 m/s

By the Pythagorean theorem

v(perpendicular) = sqr(2.04^2 - .44^2) = 1.99 m/s

The angle between the boat's velocity and the river"s velocity is

θ = 90° + arcsin(.44/2.04) = 102.46°

b)

The effective speed of the boat across the river is the perpendicular component of its velocity. So

t = d/v = 80 m/(1.99 m/s) = 40.16 s