Question

A red cross helicopter takes off from headquarters and flies 120 km at 45 degrees south of west. There it drops off some relief supplies, then flies 125 km at 20 degrees west of north to pick up three medics. If the helicoper then heads directly back to headquarters, find the distance and direction it should fly.

Answer 1

129.5km

9.78° North of east

Explanation:

Let say HQ is at the origin (x = 0, y = 0)

the coordinates of the helicopter after the 1st flight can be expressed below as

X1= -120 cos45=84.85km

Y1= -120 sin45= -84.85km

its coordinate after the 2nd flight can be expressed as

X2= x1 - 125sin20

= -84.85-42.75

=-127.6km

Y2= y1- 125cos60

=-84.5+62.5

=-22km

The distance and it's direction for it to fly back to its HQ can be calculated as

S= √(22^2 + 127.6^2 )

=129.48km

Tan θ= y2/y1

=22/127.6= 0.1724

Tan-1(0.1724)

= 9.78° North of east

Hence, the distance and direction it should fly is 129.48km and 9.78° North of east respectively