Chapter 3, Problem 57GP

To determine

To find: The speed of rain drop reference to the earth.

Answer to Problem 57GP

The speed of train will be $v_R=\frac{v_T}{\tan \theta }$ .

Explanation of Solution

Given Data:

  $\begin{array}{l}\text{Speed of train is, }{v}_T\\ \text{Making angle, }\theta \\ \text{Speed of rain is, }{v}_R\end{array}$

Calculation:

The vector for the different velocities are given as:

  

Where,

  $\begin{array}{l}{v}_T=\text{speed of train}\\ v_R=\text{speed of rain with respect to ground vertically downward}\end{array}$

Therefore, the tangent of the angle is given as:

  $\begin{array}{l}\tan \theta =\frac{v_T}{v_R}\\ v_R=\frac{v_T}{\tan \theta }\end{array}$