Question

A train is travelling due south at a rate 40 ms

-1

. The rain which is falling at an angle of 30

0 with vertical

appears falling vertically on the window pane of the train. Find the speed of the rain?​

Answer 1

Answer:

80 m/s.

Explanation:

In the question,

Speed of the train due South = 40 m/s

Angle made by the Rain with the vertical = 30°

So,

We can write from Vectors Triangle Sum property,

$v_{r,g}+v_{t,g}=v_{r,t}$

where,

$v_{r,g}$ is the velocity of rain w.r.t ground.

$v_{t,g}$ is the velocity of train w.r.t ground.

$v_{r,t}$ is the velocity of rain w.r.t train.

So,

$tan 30=\frac{v_{t,g}}{v_{r,t}}\\\frac{1}{\sqrt{3}}=\frac{40}{v_{r,t}}\\v_{r,t}=40\sqrt{3}$

Therefore, the velocity of the Rain w.r.t Train is,

$40\sqrt{3}$

Now,

Using the Pythagoras theorem,

$v_{r,g}^{2}=40^{2}+(40\sqrt{3})^{2}\\v_{r,g}=80\,m/s$

Therefore, the Speed of the Rain is 80 m/s.