Question

A car with a vertical windshield moves in a rain storm at a speed of 40km/hr. the rain drops fall vertically with a constant speed of 20m/s. the angle at which rain drops strike the windshield is

Answer 1

Answer:tan theta= 5/9

Explanation:

Answer 2

The angle at which rain drops strike the windshield is $tan^{-1}(\frac{5}{9})$

Given : A car with a vertical windshield moves in a rain storm at a speed of 40km/hr

The rain drops fall vertically with a constant speed of 20m/s

To Find : The angle at which rain drops strike the windshield

Solution : The angle at which rain drops strike the windshield is $tan^{-1}(\frac{5}{9})$

It is given that a car with a vertical windshield moves in a rain storm at a speed of 40km/hr  and the rain drops fall vertically with a constant speed of 20m/s

We have to find the angle at which rain drops strike the windshield

Now in the given figure OA represents the raindrop falling vertically

with constant speed of 20 m/s

and OB represents the a car with a vertical windshield moves in a rain storm at a speed of 40km/hr = 40 × $\frac{5}{18}$ m/s = $\frac{100}{9}$ m/s

Let theta be the angle between rain drop and the windshield

So tan theta = $\frac{CA}{OA}$

Since OABC is a parallelogram so OB = AC = $\frac{100}{9}$

So tan theta = $\frac{100}{(9) 20}$

tan theta = $\frac{5}{9}$

theta = $tan^{-1}(\frac{5}{9} )$

So the angle at which rain drops strike the windshield is $tan^{-1}(\frac{5}{9})$

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