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The angles made by the windscreens of two motorcars with horizontal are $β_{1} = 30 º$ and $β_{2} = 15 º$ respectively. The first car is travelling with a velocity $v_{1}$ horizontally. The second car is travelling with a velocity $v_{2}$ in the same direction. The hail stones are falling vertically. Both the drivers observe that the hail stones rebound vertically after elastic collision with the windscreen. Find the ratio of $v_{1} / v_{2}$ .

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Detailed Solution

The hail stones fall along AB and rebound along BC. Velocity of

stones wrt car must make an angle $2 β$ with vertical.

For first car $2 β = 60 º$

$∴ \tan 60 º = \frac{v_{1}}{v_{H}}$

For second car $2 β = 30 º$

$∴ \tan 30 º = \frac{v_{2}}{v_{H}}$

$∴ \frac{v_{1}}{v_{2}} = \frac{3}{1}$

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