Jerome and Paul are competitive brothers. They live on a small farm on the north

Question

Jerome and Paul are competitive brothers. They live on a small farm on the northern bank of a river that runs purely east and west and that flows to the east at a rate of 1.150  m/s .The brothers have run some time trials on the farm pond, and they know that, in still water, Jerome can paddle the family canoe at a steady rate of 2.650  m/s for a considerable length of time. When younger brother Paul runs a considerable distance, it turns out that he can maintain just this same pace.

In which direction must they head if they wish to paddle directly to Uncle Leo's dock? Give the direction in terms of an angle measured to the West of the Southerly direction. Also, if they point their canoe in the optimal direction, what will be the speed of their canoe with respect to the bank as they are crossing?

Give your answer as an ordered pair, with the optimal direction in which to point their canoe first, followed by a comma, then followed by the resulting speed of the canoe with respect to the bank. Give the direction in terms of an angle measured to the West of the Southerly directio

Explanation / Answer

let v_river = 1.150 m/s

v_boat = 2.650 m/s

let theta is the angle needed to move straight towards south.

v_boat*cos(theta) = v_river

cos(theta) = v_river/v_baot

cos(theta) = 1.150/2.65

theta = cos^-1(1.15/2.65)

= 23.4 degreees south of west

= 66.6 degrees west of south

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