Question Number 69847 by Rio Michael last updated on 28/Sep/19
$${A}\:{plane}\:{is}\:{travelling}\:{at}\:\mathrm{500}{km}/{hr}\:{eastward}. \\ $$$${wind}\:{blows}\:{at}\:\mathrm{90}{km}/{hr}\:{southward}. \\ $$$${find}\:{the}\:{velocity}\:{and}\:{direction}\:{if}\:{the}\:{plane}\:{rlative}\:{to}\:{the}\:{ground}. \\ $$
Answered by MJS last updated on 28/Sep/19
$$\begin{pmatrix}{\mathrm{500}}\\{\mathrm{0}}\end{pmatrix}+\begin{pmatrix}{\mathrm{0}}\\{−\mathrm{90}}\end{pmatrix}=\begin{pmatrix}{\mathrm{500}}\\{−\mathrm{90}}\end{pmatrix} \\ $$$${v}=\sqrt{\mathrm{500}^{\mathrm{2}} +\mathrm{90}^{\mathrm{2}} }=\mathrm{10}\sqrt{\mathrm{2581}}\approx\mathrm{508}.\mathrm{035} \\ $$$$\mathrm{angle}\:=\mathrm{arctan}\:\frac{−\mathrm{90}}{\mathrm{500}}\:=−\mathrm{arctan}\:\frac{\mathrm{9}}{\mathrm{50}}\:\approx−\mathrm{10}.\mathrm{20}° \\ $$
Commented by Rio Michael last updated on 28/Sep/19
$${thanks}\:{sir} \\ $$