Rain is falling vertically with a speed of ...

Motion in a Plane

Question : 12 of 32

Marks: +1, -0

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}

in the north to south direction. What is the direction in which she should hold her umbrella?

Solution:

In figure, the rain is falling along OA with speed 30 m s

^{-1}

and woman rider is moving along OS with speed 10 m s

^{-1}

i.e. OA = 30 m s

^{-1}

& OB = 10 m s

^{-1}

. The woman rider can protect herself from the rain if she holds her umbrella in the direction of relative velocity of rain w.r.t. woman. To do so apply equal and opposite velocity of woman on the rain i.e. impress the velocity 10 m s

^{-1}

due North on rain which is represented by OC.

Now the relative velocity of rain w.r.t. woman will be represented by diagonal OD of parallelogram OADC. If

\angle AOD = \theta

, then in ΔOAD,

\tan \theta = \frac{AD}{OA} = \frac{OC}{OA}

= \frac{10}{30} = 0.3333 = \tan 18^{\circ} 26'

b = 18^{\circ}26'

with vertical in forward direction.

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