Question

Runway at airport is in $(E-W)$ direction. An aircraft is about to land with speed in air $120km/h$. If aircraft is encountering a steady side wind due north of speed $40km/h$. 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. ${19.5}^o,113m/s$
• B. ${70.5}^o,125m/s$
• C. ${19.5}^o,126.5m/s$
• D. ${70.5}^o,113m/s$

Answer 1

The correct option is D ${70.5}^o,113m/s$

$120\sin \theta =40$
$\sin \theta =\frac{1}{3}$
$\theta ={\sin }^{-1}\left(\frac{1}{3}\right)={70.5}^o$
$\cos \theta =\frac{2\sqrt{2}}{3}$
$120\cos \theta =120\times 2\times \frac{1.414}{36}$
$=113km/h$