A commuter airplane starts from an airport and takes the route shown in the figu
ID: 1592996 • Letter: A
Question
A commuter airplane starts from an airport and takes the route shown in the figure. It first flies to city A located at 200 km in a direction 40 degrees north of east. Next, it flies 170 km 17 degrees west of north to city B. Finally, it flies 165 km due west to city C.
How far away from the starting point is city C? Answer in units of km.
What is the direction of the final position vector r, measured from North? Use counterclockwise as the positive angular direction, between the limits of ?180? and +180? . Answer in units of degrees.
y (km) 200 17 LED 40 r (km) 50 100 150 200Explanation / Answer
200 km in a direction 40 degrees north of east.
170 km 17 degrees west of north to city B
65 km due west to city C
X1=200cos40=153.2
Y1=200sin 40=128.5
X2=170cos 17=162.5
Y2=170sin 17=49.7
Cz=65-(x1+x2)
=65-(153.2+162.5)
=-250.7
Co=y1+y2
=128.5+49.7
=178.7
C=undrt(Cz^2+Co^2)
=udrt(-250.7^2+178.7^2)
=307.8
Sin theta=178.7/-250.7
=-40.1 degrees
West of north
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