# An aircraf flies a $400 km/hr$ in still air. A wind of $200 \sqrt 2 km/hr$ is blowing from south. A pilot wishes to travel from A to a point B north east of A .Find the direction he must steer and time of journey if $AB=1000km$

$a)\;45^{\circ}\; from\; north , 2.61 hrs \\ b)\;60^{\circ}\; from\; north , 1.50\; hrs \\ c)\; 80^{\circ}\; from\; north , 2.15 hrs \\ d)\;75^{\circ}\; from \;north , 1.83 hrs$

Let $v_w$=Velocity of wind
The aircraft should fly along $AC$ with a velocity of $v_{aw}=400 km/hr$ so that the resultant is along $AB$
Let $v_{aw}$ makes angle $\alpha$ with $AB$
$\large\frac{AC}{\sin 45}=\frac{BC}{\sin \alpha}$
$\sin \alpha=\large\frac{BC}{AC} $$\sin 45 \qquad= \large\frac{200 \sqrt 2}{400} \times \frac{1}{\sqrt 2}=\frac{1}{2} Therefore \alpha=30^{\circ} The piolt should steer in a direction (45 + \alpha)=75^{\circ} from North towards East Also \large\frac{v_a}{\sin (180-75)}=\frac{400}{\sin 45} v_a=\large\frac{\cos 15}{\sin 45}$$\times 400$
$\quad=\large\frac{0.9659}{0.707}$
$\quad= 546.47 km/hr$
Therefore $t=\large\frac{1000}{546.47}$
$\qquad=1.83\; hr$
Hence d is the correct answer

edited Jan 26, 2014 by meena.p