Question

a person is moving on the ground with speed 5 kilometre per minute raindrops are falling vertically downwards he experiences that drops are meeting him at angle 30 degree with the vertical for what speed of man he will experience drops are meeting him at angle 30 degree with the horizontal​

Answer 1

Given:

A person is moving on the ground with speed 5 kilometre per minute raindrops are falling vertically downwards he experiences that drops are meeting him at angle 30 degree with the vertical.

To find:

Speed of man such that the rain falls at 30° to horizantal ?

Calculation:

The general case of man and rain has been illustrated in the attached photo, let Velocity of man be v_(m) and velocity of rain be v_(r) :

When $\theta$ = 30°, we can say:

$\therefore \: \tan( \theta) = \dfrac{v_{m}}{v_{r}}$

$\implies \: \tan( {30}^{ \circ} ) = \dfrac{5}{v_{r}}$

$\implies \: \dfrac{1}{ \sqrt{3} } = \dfrac{5}{v_{r}}$

$\implies \: v_{r} = 5 \sqrt{3} \: km/ min$

When $\theta$ = 60° (i.e. 30° to horizantal) we can say:

$\therefore \: \tan( \theta) = \dfrac{v_{m}}{v_{r}}$

$\implies \: \tan( {60}^{ \circ} ) = \dfrac{v_{m}}{5 \sqrt{3} }$

$\implies \: \sqrt{3} = \dfrac{v_{m}}{5 \sqrt{3} }$

$\implies \: v_{m} = 5 \sqrt{3} \times \sqrt{3}$

$\implies \: v_{m} = 5 \times 3$

$\implies \: v_{m} = 15 \: km/min$

So, required velocity of man is 15 km/min.