Question

An airplane flies 20km in a direction 60 degrees north of east, then 30 km straight east, then 10km straight north. How far and in what direction is the plane from the starting point​

Answer 1

Answer:

48.4 km, 34.3° north of east

Explanation:

Let's say east is the +x direction and north is the +y direction.

Adding up the x components of the vectors:

x = 20 cos 60 + 30 + 0

x = 40 km

Adding up the y components of the vectors:

y = 20 sin 60 + 0 + 10

y = 27.3 km

The magnitude of the displacement is:

d = √(x² + y²)

d = 48.4 km

The direction is:

θ = atan(y/x)

θ = 34.3° north of east