Ncert Exercises & Solutions

4.12 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?

NEETprep Answer:

The described situation is shown in the given figure

Here,

$\begin{array}{l} v_{c} = Velocity of the cyclist \\ v_{r} = Velocity of falling rain \end{array}$

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

\begin{array}{l} v = v_{r} + (- v_{c}) \\ = 30 + (- 10) = 20 m / s \\ \tan θ = \frac{v_{c}}{v_{r}} = \frac{10}{30} \\ θ = \tan^{- 1} (\frac{1}{3}) \\ = \tan^{- 1} (0.333) \approx 18^{\circ} \end{array}

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.

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