A woman sailing a boat at night is following directions to a dock. The instructions read to first sail 27.5 m in a direction 66.0° north of east from her current location, and then travel 30.0 m in a direction 112° north of east (or 22.0° west of north). If the woman makes a mistake and travels in the opposite direction for the second leg of the trip, where will she end up? Compare this location with the location of the dock.

Strategy

We can represent the first leg of the trip with a vector A, and the second leg of the trip with a vector B. The dock is located at a location A + B. If the woman mistakenly travels in the opposite direction for the second leg of the journey, she will travel a distance B (30.0 m) in the direction 180°-112° = 68° south of east. We represent this as -B, as shown below. The vector-B has the same magnitude as B but is in the opposite direction. Thus, she will end up at a location A+(-B), or A-B.

We will perform vector addition to compare the location of the dock, A + B, with the location at which the woman mistakenly arrives, A + (-B).

Transcribed Image Text:

A LE 66° X YA A = 27.5 m B B = 30.0 m 112°