Question

Rain is falling vertically at speed of $10m/s$ and a man is moving with velocity $6m/s$. Find the angle at which the man should hold his umbrella to avoid getting wet.

• A. $si{n}^{-1}\left(\frac{3}{5}\right)$
• B. $co{s}^{-1}\left(\frac{3}{5}\right)$
• C. $ta{n}^{-1}\left(\frac{4}{5}\right)$
• D. $ta{n}^{-1}\left(\frac{3}{5}\right)$

Answer 1

The correct option is D $ta{n}^{-1}\left(\frac{3}{5}\right)$

$\overline{tain}=-10\hat{j}\Rightarrow {\overline{v}}_{man}=6\hat{j}$
${\overline{v}}_{r.w.r.t.man}=-10\hat{j}-6\hat{i}$
$tan\theta =\frac{6}{10}\Rightarrow \theta =ta{n}^{-1}\left(\frac{3}{5}\right)$
Where $\theta$ is angle with verticle

$V_r$=10$\frac{m}{sec}$
$V_m$=6$\frac{m}{sec}$
$V_{r,m}$=$V_r$$-$$V_m$
$V_{r,m}$$=-10$$\hat{j}$$-(+6$$\hat{i}$)
$tan\theta$=$\frac{6}{10}$
$\theta$=$ta{n}^{-1}$($\frac{3}{5}$)