Question

A car is moving in a rainstorm at a speed of $60\text{km/h}$. The rain drops fall vertically w.r.t the ground with a constant speed of $15\text{m/s}$. The angle with the vertical at which raindrops strike the car is

• A. ${\tan }^{-1}\frac{10}{9}$
• B. ${\sin }^{-1}\frac{10}{9}$
• C. ${\tan }^{-1}\frac{9}{10}$
• D. ${\cos }^{-1}\frac{10}{9}$

Answer 1

The correct option is A ${\tan }^{-1}\frac{10}{9}$


Velocity of car = $v_c=60\text{km/h}=50/3\text{m/s}$
Velocity of rain drops, $v_r=15\text{m/s}$
From the figure, we get
$\tan \theta =\frac{v_c}{v_r}=\frac{50/3}{15}=\frac{10}{9}$
$\theta ={\tan }^{-1}\left(\frac{10}{9}\right)$