Question

Answer all Parts:

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 1.450 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 2.600 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.

Parts B and C - The Brothers Paddle Together Across the River and Slightly Downriver The brothers like to visit their Uncle Leo who lives on the southern bank of the river. The river is wide at this point, 1310.0 m across, and their uncle's dock is 195.0 m to the east of the point which is directly across the river from the brothers' house. Paul is not nearly as strong a paddler as is Jerome, but paddling together they can maintain a paddling speed of 2.860 m/s in the farm pond. Jerome knows that if they point their canoe due south, they will always end up to the east of Uncle Leo's dock by the time they have paddled across the river. He wants to know in which direction they should head to arrive exactly at Uncle Leo's dock without any wasted effort. Paul is finally able to determine the proper direction by using the Law of Sines, which he has learned in his high school geometry class. Make a proper drawing to express the sum of velocities for this problem, and figure out how Paul was able to determine the direction.

Part B: 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 direction.

Part C: If they point their canoe in the optimal direction, how long will it take for them to cross the river?

Part D: Once they have finished their visit with Uncle Leo, in which direction must the brothers head in order to return directly to their own dock on the north shore of the river? Also, if they point their canoe in the optimal direction for the return trip, then 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 their canoe with respect to the bank. Give the direction in terms of an angle measured to the West of the Northerly direction.

Part E: If they point their canoe in the optimal direction for the return trip, then how long will the return trip take?

Answer 1

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