Conceptualize Imagine moving across a river while the current pushes you down th

Question

Conceptualize Imagine moving across a river while the current pushes you down the river. You will not be able to move directly across the river, but will end up downstream as suggested in figure (a).

Categorize Because of the separate velocities of you and the river, we can categorize this problem as one involving relative velocities.

Analyze We know br, the velocity of the boat relative to the river, and rE, the velocity of the river relative to the Earth. What we must find is bE, the velocity of the boat relative to the Earth. The relationship between these three quantities is bE = br + rE. The terms in the equation must be manipulated as vector quantities; the vectors are shown in figure (a). The quantity br is due north; rE is due east; and the vector sum of the two, bE, is at an angle ? as defined in figure (a).
(A) If the boat heads due north, determine the velocity of the boat relative to an observer standing on either bank.
Find the speed bE of the boat relative to the Earth using the Pythagorean theorem:
bE = (br2 + rE2)1/2 = km/h
Find the direction of bE:
? = tan-1(rE / br) =

Explanation / Answer

Speed of boat relative to shore = (3.52+3.12) = 4.68 m/s

Direction = atan(3.5/3.1) = 48.7 deg south of east.

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