Answer to Question #120399 in Other for Nimra

Question

An airplane pilot wishes to fly due West. A wind of 80.0 km/h is blowing towards the South.(a) if the airspeed of the plane (its speed in still air) is 320.0 km/h in which direction should the pilot head ? (B) what is the speed of the plane over the ground? draw a vector diagram.

Answer 1

Let

$\overrightarrow{v}_{p/g}=$ the velocity of the plane relative to the ground (due west),

$\overrightarrow{v}_{p/a}=$ the velocity of the plane relative to the air ($|\overrightarrow{v}_{p/a}|=320.0\ km/h$ ), and

$\overrightarrow{v}_{a/g}=$ the velocity of the air relative to the ground ($|\overrightarrow{v}_{a/g}|=80.0\ km/h,$ due south).

The velocity vector addition

$$\overrightarrow{v}_{p/a}+\overrightarrow{v}_{a/g}=\overrightarrow{v}_{p/g}$$

a)

$$\sin \theta={|\overrightarrow{v}_{a/g}|\over |\overrightarrow{v}_{p/a}|}={40 km/h\over 320 km/h}=0.25$$

$$\theta=14.5\degree,\text{north of west}$$

b)

$$|\overrightarrow{v}_{p/q}|=\sqrt{(|\overrightarrow{v}_{p/a}|)^2-(|\overrightarrow{v}_{a/g}|)^2}=$$

$$=\sqrt{(320 \ km/h)^2-(80\ km/h)^2}=80\sqrt{15}\ km/h\approx$$

$$\approx310\ km/h$$