Question

An airplane undergoes the following displacements: First, it flies 45 km in a direction 30° east of north. Next, it flies 76 km due south. Finally, it flies 100 km 30° north of west.

A) Using analytical methods, determine how far the airplane ends up from its starting point.

Answer 1

Use pythagoras' theorem, to find the horizontal and vertical components of the movement =)

First, make north and east positive, and try to draw it's track.
OK
So, cos(60) = (distance travelled due east)/(59)
So, cos(60)*45 = 22.5 km east, and sin(60)*45 = distance north = 38.97km north

Now, you can minus the 38.97km from the 76km south (south is negative remember =) )
So now, we are at the point, 37.03km south of where we started, and still 22.5km east from where we started.
Now for the last movement.
sin(30)*100 = distance north = 50km (we can think of this as positive)
cos(30)*100 = distance west = 86.602km (we can think of this as negative)
So, since we are at -37.03 south, we add the 50 to get 12.97km north of where we started
and we are at 22.5km east, so minus 86.602 = -64.10km west.
So now our point is (12.97,-64.10)
now sub this into another triangle, and solve for the hypotenus =D
So, your total displacement, is (12.97^2 + -64.10^2)^(1/2)
= 65.30