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18 September, 18:11

A cyclist rides her bike 7 mi east, and then 2 mi north before taking a break. Then she rides 5 mi east and then 3 mi north. What are the magnitude and direction of the cyclist's resultant displacement?

magnitude: 13.0 mi; direction: 22.6° north of east

magnitude: 13.0 mi; direction: 67.4° north of east

magnitude: 10.9 mi; direction: 67.4° north of east

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  1. 18 September, 18:13
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    Eastward rides = 7+5 = 12 miles

    Northward rides = 2+3 = 5 miles

    This forms a right angled triangle.

    The resultant triangle has legs with 12 mi and 5 mi. The hypotenuse is the resultant. Then,

    Resultant = Sqrt (12^2+5^2) = 13 mi

    The angle formed by the resultant to the east direction is given by:

    Sin Ф = 5/13 = > Ф = Sin ^-1 (5/13) = 22.62°

    The correct answer is given by option 1: magnitude = 13.0 mi; direction = 22.6° North of East.
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