Question

A person is walking in rain feels the relative velocity of rain is twice to his velocity . at which angle he should hold umbrella with vertical if he moves forward
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Answer 1

We can assume a right triangle there, whose,

• base is given by the velocity of the person.

• the altitude is given by the actual velocity of the rain (since rain is falling vertically downwards to the ground).

• the hypotenuse is given by the relative velocity of rain (i.e., velocity wrt the person).

Let 'x' be the angle (acute) made by the relative velocity of rain with the vertical (i.e., with the actual velocity of the rain), by which the person has to hold his umbrella. Then,

$\quad$

$\sin x=\dfrac {\text{Velocity of person}}{\text {Relative velocity of rain}}$

$\quad$

Since the relative velocity of rain is twice the velocity of the person,

$\quad$

$\sin x=\dfrac {1}{2}$

$\quad$

This implies,

$\quad$

$\underline {\underline {x=30^{\circ}}}$