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A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of 2m/s. Now the wind screen is placed at angle $α$ with the vertical such that the rain drops falling vertically downwards with velocity 6 m/s strike the wind screen perpendicularly. What is the value of tan $α$ ?

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answer is 3.

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Detailed Solution

$v_{r} = 6 m / s, v_{c} = 2 m / s, {\vec{v}}_{rc} = {\vec{v}}_{r} - {\vec{v}}_{c}$

where ${\vec{v}}_{rc}$ is relative velocity of rain w.r.t. car. It should be perpendicular to wind screen.

So $\tan α = \frac{v_{r}}{v_{c}} = \frac{6}{2} = 3$

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