During a hike, a person walks 7 km east and then 24 km north. Which description best matches the person’s resultant displacement vector?
A vector of 25 km pointing northeast from the starting point
East and north are perpendicular, so the resultant is the hypotenuse: \(\sqrt{7^2+24^2}=\sqrt{49+576}=\sqrt{625}\) = 25 km.
The resultant points between east and north (north of east) from the starting point.
31 km is the total distance walked, not the displacement.
Hence, the displacement is a vector of 25 km pointing northeast from the starting point.
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