Question

The compass needle of the airplane shows that it is heading due North and speedometer indicates a velocity $240km{h}^{-1}$. Wind is blowing $100km{h}^{-1}$ due east. Find the velocity of airplane with respect to earth.

• A. $260m{s}^{-1},{23}^{\circ }$ East of North
• B. $260m{s}^{-1},{23}^{\circ }$ West of North
• C. $260m{s}^{-1},{32}^{\circ }$ East of North
• D. none of these

Answer 1

Answer: (A)

$260m{s}^{-1},{23}^{\circ }$ East of North

Net velocity of aeroplane $\overrightarrow{v}=240\hat{i}+100\hat{j}$

$v=\left|\overrightarrow{v}\right|=\sqrt{{240}^2+{100}^2}$

$\theta ={\tan }^{-1}\frac{100}{240}={23}^o$