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Mathematics-Online problems:

Interactive Problem 613: Flight Path of Starting Airplanes

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
From an airfield (located at the origin of the coordinate system) airplanes take off in northerly direction (y-direction) at an angle of climb of 30$ ^\circ.$ On their way up, they cross an air lane that runs 10 km further north at an altitude of 10 km and which is passed by airplanes from west to east (x-direction) every 5 minutes at a velocity of 600 km/h.

\includegraphics[bb=140 483 591 714,clip,width=.8\linewidth]{Flugplatz_Bild1_en}

Determine the straight line $ g_1$ describing the flight path of the climbing airplanes and the straight line $ g_2$ describing the air lane.
Determine the distance $ s_1$ between the straight lines.
If optimal departure times are chosen, what is the distance $ s_2$ between the climbing and the crossing airplanes?


Answer:

$ g_1:$ $ \left( \begin{array}{c} x \\ y \\ z \end{array}\right)$ $ =$
$ \left( \rule{0pt}{8ex}\right.$
0
$ \left. \rule{0pt}{8ex}\right)$
$ + \,\, t \left( \rule{0pt}{8ex}\right.$
$ 10 / \sqrt{3}$
$ \left. \rule{0pt}{8ex}\right)$
$ g_2:$ $ \left( \begin{array}{c} x \\ y \\ z \end{array}\right)$ $ =$
$ \left( \rule{0pt}{8ex}\right.$
0
$ \left. \rule{0pt}{8ex}\right)$
$ + \,\, t \left( \rule{0pt}{8ex}\right.$
$ 1$
$ \left. \rule{0pt}{8ex}\right)$

$ s_1$ $ =$
$ s_2$ $ =$

(The results should be correct to two decimal places.)


   

(From: Day of Mathematics 2004)
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  automatically generated: 2/ 6/2018