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Question Number 69847 by Rio Michael last updated on 28/Sep/19

A plane is travelling at 500km/hr eastward.  wind blows at 90km/hr southward.  find the velocity and direction if the plane rlative to the ground.

$${A}\:{plane}\:{is}\:{travelling}\:{at}\:\mathrm{500}{km}/{hr}\:{eastward}. \\ $$$${wind}\:{blows}\:{at}\:\mathrm{90}{km}/{hr}\:{southward}. \\ $$$${find}\:{the}\:{velocity}\:{and}\:{direction}\:{if}\:{the}\:{plane}\:{rlative}\:{to}\:{the}\:{ground}. \\ $$

Answered by MJS last updated on 28/Sep/19

 (((500)),(0) )+ ((0),((−90)) )= (((500)),((−90)) )  v=(√(500^2 +90^2 ))=10(√(2581))≈508.035  angle =arctan ((−90)/(500)) =−arctan (9/(50)) ≈−10.20°

$$\begin{pmatrix}{\mathrm{500}}\\{\mathrm{0}}\end{pmatrix}+\begin{pmatrix}{\mathrm{0}}\\{−\mathrm{90}}\end{pmatrix}=\begin{pmatrix}{\mathrm{500}}\\{−\mathrm{90}}\end{pmatrix} \\ $$$${v}=\sqrt{\mathrm{500}^{\mathrm{2}} +\mathrm{90}^{\mathrm{2}} }=\mathrm{10}\sqrt{\mathrm{2581}}\approx\mathrm{508}.\mathrm{035} \\ $$$$\mathrm{angle}\:=\mathrm{arctan}\:\frac{−\mathrm{90}}{\mathrm{500}}\:=−\mathrm{arctan}\:\frac{\mathrm{9}}{\mathrm{50}}\:\approx−\mathrm{10}.\mathrm{20}° \\ $$

Commented by Rio Michael last updated on 28/Sep/19

thanks sir

$${thanks}\:{sir} \\ $$

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