Chapter 5, Problem 28A

Rain falling vertically will make vertical streaks on a car’s side window. However, if the car is moving, the streaks are slanted. If the streaks from a vertically falling rain make $45°$ streaks, how fast is the car moving compared with the speed of the falling rain?

To determine

To compare: Speed of car with speed of rain.

Answer to Problem 28A

Both car and rain have same velocity.

Explanation of Solution

Given :

Angle between both velocity is, $\theta =45°$

Formula used :

  $\tan \theta =\frac{v_y}{v_x}$

Where, $v_y$ is vertical speed and $v_x$ is horizontal speed.

Calculation :

As rain is falling vertically therefore its speed will be, $v_y$

And car is moving horizontally therefore its speed be, $v_x$

Now, substituting the value of $\theta$ and solve.

  $\begin{array}{l}\tan 45°=\frac{v_y}{v_x}\\ 1=\frac{v_y}{v_x}\\ v_y=v_x\end{array}$

Conclusion :

Therefore, speed of both rain falling and car will be same.