Question

An airplane pilot sets a compass course due west and maintains an airspeed of $240km/h{r}^{-}1$. After flying for $\frac{1}{2}hr$, he finds himself over a town is $150km$ west and $40km$ south of his starting point.
1. Find the wind velocity, in magnitude and direction.
2. If the wind velocity were 120 $km/hr$ due south, in what direction should the pilot set his course in order to travel due west? Take the same airspeed.

Answer 1

$d^2=\left({150}^2\right)+\left({40}^2\right)$

$22500+1600$

$24100k{m}^2$

$d=\sqrt{24100}=155km$

$\theta =ta{n}^{-1}\left(\frac{40}{150}\right)ta{n}^{-1}0.2667$

$={15}^0$

velocity of pilot with respective to ground $\left(\overrightarrow{v_1}\right)$

$\left(\overrightarrow{v_1}\right)$

$=\frac{155}{0.5}=310km{h}^{-1}$

$\left(\overrightarrow{v_2}\right)bevelocityofairand\left(\overrightarrow{v_3}\right)bevelocityofwind$

cosine law

${\overrightarrow{v^{}}}_3^2{\overrightarrow{v_1}}^2{\overrightarrow{v_2}}^2-2\overrightarrow{v_1}\overrightarrow{v_2}cos{15}^0$

$\left({240}^2\right)+\left(310^2\right)-2\left(210\right)\left(310\right)\left(0.9659\right)$

$57600+96100-143730$

$9970$

$\left(\overrightarrow{v_3}\right)=100km{h}^{-1}$