Question

Rain is falling vertically with a speed of 30 m/s and
wind is blowing horizontally from north to south with a
speed of 10 m/s. In which direction should a person
standing in the open hold his umbrella?​

Answer 1

AnswEr :

• A person should hold the umbrella towards the south, also, at an angle of 18° w. r. t the vertical.

• Reason : If the person holds the umbrella as per the answer then he might be get protected from the rain!!

Given :

• Speed of rain(Vr) = 30 m/s

• Speed of wind(Vw) = 10 m/s

To Find :

• In which direction should a person, standing in the open hold his umbrella to get protected from the rain = ?

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Concept to be used :

★ Relative Velocity :

The relative velocity of an object is the velocity that an object A would appear to an observer on the object B further vice versa !!

In simple words you can say that, relative velocity is the vector difference between the velocities of any 2 bodies

It is given as :

Relative velocity = velocity of object A - velocity of object B.

which gives,

$\large \dag \ {\boxed{\rm{v_{AB} = v_A - v_B}}}$

So, by applying this concept let's solve the question..!!

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Let Vw be the velocity of wind and Vr be the velocity of rain itself.

Now,

According to the direction of the relative velocity (v) of the rain with respect to that of the person,

➝ tan θ = Velocity of the wind/ velocity of the rain

➝ tan θ = Vw/Vr

➝ tan θ = 10/30

➝ tan θ = 1/3

➝ θ = 18°

Therefore, the person should hold the umbrella toward the south, at an angle of 18°.

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