Question

An airplane pilot sets a compass course due west and maintains an air speed of 240 km/h. After flying for $\frac{1}{2}h,$ he finds himself over a town that is 150 km west and 40 km south of his starting point. The wind velocity (with respect to ground).

• A. $100km/h,{37}^{o}WofS$
• B. $100km/h,{37}^{o}SofW$
• C. $120km/h,{37}^{o}WofS$
• D. $120km/h,{37}^{o}SofW$

Answer 1

Answer: (A)

$100km/h,{37}^{o}WofS$

$d^2={150}^2+{40}^2$

$=24100k{m}^2$

$d=155km$

$\theta ={\tan }^{-1}\left(\frac{40}{150}\right)={15}^0$

Velocity & pilot w.r.t ground $\left(\overline{v_1}\right)$

$\frac{-155}{0.5}=310km{h}^{-1}$

$v_2\Rightarrow$ velocity of $e{u}^r$,$v_3\to$ velocity of wind w.r.t ground

$\overline{v_3}=\overline{v_1}+\overline{v_2}=2\overline{v_1}.\overline{v_2}$

$={240}^2+{310}^2-2\times 210\times 310\times 0.9659$

$\overline{v_3}=100km/hr$