Question

A lorry with a vertical wind shield moves on a horizontal road in a rainstorm at a speed of $15\text{m/s}$. The rain drops fall vertically with a speed of $30\text{m/s}$. The angle at which the rain drops strike the wind shield for the driver is :

• A. $\theta ={\tan }^{-1}\frac{2}{3}$
• B. $\theta ={\tan }^{-1}\frac{1}{2}$
• C. $\theta ={\tan }^{-1}\frac{1}{3}$
• D. $\theta ={\tan }^{-1}\frac{1}{4}$

Answer 1

The correct option is B $\theta ={\tan }^{-1}\frac{1}{2}$


As observed by the driver, the rain drops will strike the windshield in the direction of velocity of rain w.r.t lorry$\left(v_{rl}\right)$

${\overrightarrow{v}}_{rl}=$Velocity of rain w.r.t lorry
${\overrightarrow{v}}_{rg}=$Velocity of rain w.r.t ground
${\overrightarrow{v}}_{lg}=$Velocity of lorry w.r.t ground

Using equation for relative velocity,
${\overrightarrow{v}}_{rg}={\overrightarrow{v}}_{rl}+{\overrightarrow{v}}_{lg}$

From the vector triangle as shown in figure,

$\tan \theta =\frac{|{\overrightarrow{v}}_{lg}|}{|{\overrightarrow{v}}_{rg}|}=\frac{15}{30}=\frac{1}{2}$

$\Rightarrow \theta ={\tan }^{-1}\frac{1}{2}$

Hence, option $\left(\text{B}\right)$ is the right choice.

$$\begin{array}{c}\text{Why this question?}\\ \text{When rain drops are falling vertically w.r.t the ground,}\\ \text{then they will appear to fall at an angle with respect to a moving}\\ \text{observer due to addition of the velocity of observer in the velocity of rain w.r.t ground.}\end{array}$$