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Home » Rain is falling vertically with a speed of 30 m s^{-1} . A woman rides a bicycle with a speed of 10 m s^{-1}ms −1 in the north to south direction. What is the direction in which she should hold her umbrella?
Rain is falling vertically with a speed of 30 m s^{-1} . A woman rides a bicycle with a speed of 10 m s^{-1}ms −1 in the north to south direction. What is the direction in which she should hold her umbrella?
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
Rain is falling vertically with a speed of 30 m s^{-1} . A woman rides a bicycle with a speed of 10 m s^{-1}ms −1 in the north to south direction. What is the direction in which she should hold her umbrella?

Answer :

Here,

vc

denotes theVelocity of the cyclist = 10 m/s

vr

denotes the Velocity of falling rain = 30 m/s

The woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to her in order to protect herself from the rain. Therefore, relative velocity becomes

v = 30 + (-10)

v = 20 m/s

\therefore \tan \theta =\frac{{{v}_{c}}}{{{v}_{r}}}

\tan \theta =\frac{10}{30}

\theta ={{\tan }^{-1}}\left( \frac{1}{3} \right)

\theta ={{18}^{\circ }}

As a result, the woman must hold the umbrella at an angle of about 18 degrees with the vertical, facing south.

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