Answer to Question #136146 in Mechanics | Relativity for Andrea

Question

A jet airliner moving initially at 399 mph (with respect to the ground) to the east moves into a region where the wind is blowing at 552 mph in a direction 72◦ north of east. What is the new speed of the aircraft with respect to the ground? Answer in units of mph.

Answer 1

Solution

Given angle $\theta=72^0$

Speed of aircraft

$V=\sqrt{v_a^2+v_w^2+2v_av_w\cos\theta}$

Where $v_a, v_w$ are speed of airlines and wind with respect to ground.

Therefore new speed of airlines ith respect to ground can be expressed as

$V=\sqrt{(399)^2+(552)^2+2\times (399)\times (552)cos72^°}$

$V=774.6 mph$