A canoe has a velocity of 0.510 m/s southeast relative to the earth. The canoe i

Question

A canoe has a velocity of 0.510 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.520m/s east relative to the earth. Find the magnitude of the velocity v c/r of the canoe relative to the river. Express your answer in meters per second. Your answer -395 m/s was either rounded differently or used a different number of significant figures than required for this part. Find the direction of the velocity of the canoe relative to the river. Express your answer as an angle measured south of west.

Explanation / Answer

let east direction be represented by x axis and unit vector along x axis is i

let south direction be represented by y axis and unit vector along y axis is j

then vc/c = 0.51cos45 i + 0.51 sin45 j = 0.361 i + 0.361 j m/s

vr/c = 0.520 i

=> Vc/r (velocity conoe wrt to river) = Vc/c - V r/c = -0.159 i + 0.361 j m/s

=> direction = arctan(0.361/0.159) south of west

direction = 66.229 degree C south of west

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