Answer to Question #101339 in Physics for Alex

Question

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?

Answer 1

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=17.80⁰ North of east