Answer to Question #253755 in Physics for malice

Question

Two airplanes leave an airport at the same
time. The velocity of the first airplane is
710 m/h at a heading of 20.7
à ƒ ƒ ¢ — ¦
. The velocity
of the second is 560 m/h at a heading of 107à ƒ ƒ ¢ — ¦
.
How far apart are they after 1.8 h?

Answer 1

Find the angle between the bearings of the airplanes:

$$\theta=107°-20.7°=86.3°.$$

Apply the law of cosines:

$$D=\sqrt{(v_1t)^2+(v_2t)^2-2v_1v_2t^2\cos\theta}=1576\text{ miles}.$$