Question

Runway at airport is in $$(E-W)$$ direction. An aircraft is about to land with speed in air $$120\ km/h$$. If aircraft is encountering a steady side wind due north of speed $$40\ km/h$$. At what angle $$\theta$$ with runway should the pilot direct the aircraft so that the resultant velocity is parallel to the runway and speed at touch down respectively are

A
19.5o,113 m/s
B
70.5o,125 m/s
C
19.5o,126.5 m/s
D
70.5o,113 m/s

Solution

The correct option is D $$70.5^{o}, 113\ m/s$$$$120\sin \theta=40$$$$\sin \theta=\dfrac{1}{3}$$$$\theta=\sin^{-1}\left(\dfrac{1}{3}\right)=70.5^{o}$$$$\cos \theta=\dfrac{2\sqrt{2}}{3}$$$$120\cos \theta=120\times 2\times \dfrac{1.414}{36}$$$$=113\ km/h$$Physics

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