Chapter 3, Problem 38P

To determine

The speed of snowflakes relative to car and relative to the ground..

Answer to Problem 38P

The speed of rain relative to the ground is 14.43m/s.

The speed of rain relative to the car is 28.87m/s.

Explanation of Solution

Given Data:

Car is going south on the highway at 25m/s in the snowstorm.

Snow was coming down vertically but passing the window of the moving car at an angle of 30^o.

Calculation:

The velocity diagram is drawn as:

  

Where,

  $\begin{array}{l}{v}_c=25\text{m/s=veloctiy of the car}\\ v_R=\text{Velocity of te rain with respect ot the ground}\\ v_{RC}=\text{Velcoty of the rain with respect to the car}\end{array}$

From the figure:

  $\begin{array}{l}\tan {30}^0=\frac{v_R}{v_C}\\ v_R=v_C\tan {30}^0\\ =25\left(\frac{1}{\sqrt{3}}\right)\\ =14.43\text{m/s}\end{array}$

Hence, the speed of the rain relative to the ground is 14.43m/s vertically downward.

From the figure:

  $\begin{array}{l}\cos {30}^o=\frac{v_C}{v_{RC}}\\ v_{RC}=\frac{v_C}{\cos {30}^o}\\ v_{RC}=\frac{25}{\frac{\sqrt{3}}{2}}\\ v_{RC}=28.87\text{m/s}\end{array}$

Therefore, the rain relative to the car will be 28.87m.s at 30-degree to the horizontal.