Question

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

Answer 1

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.