A boat can travel at a speed of 4.3 m/s in still water. A river that is 150 m wi

Question

A boat can travel at a speed of 4.3 m/s in still water. A river that is 150 m wide has a current that flows 1.15 m/s due West.
a) If the boat points its bow directly across the river, how fast does the boat travel relative to the shore?

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

c) How far downriver will it land (the distance on the bank from the point directly across from the starting point to the landing point)?

d) At what angle should the boat be pointed in order to arrive at a point directly across from the starting point? Assume North is directly across the river.

Explanation / Answer

(a) Relative vel. = sqrt(4.3^2 + 1.15^2) = 4.45 m/s (b) time = 150/4.3 = 34.88 s (c) 34.88*1.15 = 40.12 m (d) sin^-1(1.15/4.3) = 15.51 (e) vel in horizontal direction = sqrt(4.3^2 - 1.15^2) = 4.14 m/s time taken = 150/4.14 = 36.2 s

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