Question #101339

A ferry leaves the terminal and travels 124km in a direction 12.0 north of west to island A. After a short stop, the ferry travels 85.4km in a direction 26.0 west of south to island B. The ferry then completes the round trip by returning directly to the terminal.
a)Draw a vector diagram that describes the entire journey.
b)What is the displacement (magnitude and direction) of the ferry in the last trip?

Expert's answer

From the diagram,

@$R *cos(x)= 124cos(12)+85.4sin(26)\\ R*sin(x)=85.4cos(26)-124sin(12) \\@$

Solving this gives,

R=166.7km

x=17.80^{0} North of east

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