Question

A man running on a horizontal road at $8km/h$ finds the rian falling vertically. He increases his speed to $12km/h$ and finds that the drops make angle ${30}^o$ with the vertical. Find the speed and direction of the rain with respect to the road.

• A. $4Kmph,{\tan }^{-1}\left(2\right)$ witih the vertical
• B. $4Kmph,{\tan }^{-1}\left(1/2\right)$ witih the vertical
• C. $8Kmph,{\tan }^{-1}\left(3/2\right)$ witih the vertical
• D. $4\sqrt{7}Kmph,{\tan }^{-1}\left(2/\sqrt{3}\right)$ witih the vertical

Answer 1

The correct option is D $4\sqrt{7}Kmph,{\tan }^{-1}\left(2/\sqrt{3}\right)$ witih the vertical

$\begin{array}{c}\Rightarrow \tan {30}^0=\frac{12-u\sin \theta }{u\cos \theta }\\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{4}{u\cos \theta }\\ \Rightarrow u\cos \theta =4\sqrt{3}.........\left(2\right)\end{array}$

Equation $\left(1\right)÷\left(2\right)$

$\begin{array}{c}\tan \theta =\left(\frac{2}{\sqrt{3}}\right)\\ \&u=4\sqrt{7}\end{array}$

$\therefore$ Option $D$ is correct.