Question

A man is walking due east at a rate of $5km/h$ and the rain appears to be falling vertically with a speed of $12km/h$. Calculate the direction of rain.

• A. ${22}^o{37}^{\prime }$ east of vertical
• B. ${22}^o{22}^{\prime }$ east of vertical
• C. ${37}^o{68}^{\prime }$ east of vertical
• D. ${68}^o{22}^{\prime }$ east of vertical

Answer 1

The correct option is A ${22}^o{37}^{\prime }$ east of vertical

$V_{Rain,Person}=V_{Rain}-V_{Person}=-12\hat{j}$ (vertically down)

Thus, $V_{Rain}-\left(5\hat{i}\right)=-12\hat{j}$ or, $V_{Rain}=5\hat{i}-12\hat{j}$

Thus, direction is $ta{n}^{-1}\left(\frac{5}{12}\right)={22}^o{37}^{\prime }$ east of vertical $(+5,-12)$ means $4^{th}$ quadrant, thus east of vertical.