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: 10.9 mi; direction: 22.6° north of east



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



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



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

Answer 1

Answer:

D 13.0mi, dir 22.6° north of east

Explanation:

Total movement east is 7+5 miles, or 12 miles. Total movement north is 2+3 miles, or 5 miles. The total displacement, as the crow flies, is of $\sqrt{12^2+5^2} =13$miles. The angle is the inverse tangent of north/east, or $tan^{-1} \frac 5 {12} =22.62°$