Question

A steamer is moving due east with $10km/h$. To a man in the steamer the wind appears to blow at $5km/h$ due north. Find the velocity of the wind.

• A. $5\sqrt{5}m{s}^{-1}{26.56}^{\circ }$ North of east
• B. $5m{s}^{-1}{53.13}^{\circ }$ North of east
• C. $5\sqrt{5}m{s}^{-1}{53.13}^{\circ }$ North of east
• D. $5m{s}^{-1}{26.56}^{\circ }$ North of east

Answer 1

Answer: (A)

$5\sqrt{5}m{s}^{-1}{26.56}^{\circ }$ North of east

$V_{ws}-V_w-V_s\Rightarrow (V_{wx}\hat{i}+V_{wy}\hat{j})-10\hat{i}=5\hat{j}$
$V_{wx}\hat{i}+V_{wy}\hat{j}=5\hat{j}+10\hat{i}$ or
$|V_w|=5\sqrt{5};\tan \theta =\frac{1}{2}$ $⟹\theta ={26.56}^{\circ }$

i.e wind is blowing at $5\sqrt{5}m{s}^{-1}{26.56}^{\circ }$ North of east