Question

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

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Solution

## Step 1: GivenSpeed of the car, ${v}_{c}=40km/hr=\frac{100}{9}m/s$Speed of the raindrop, ${v}_{r}=20m/s$Step 2: Draw the free body diagramStep 3: Determine the angleThe resultant angle is given by, $\mathrm{tan}\theta =\frac{{v}_{c}}{{v}_{r}}\phantom{\rule{0ex}{0ex}}=\frac{\frac{100}{9}}{20}\phantom{\rule{0ex}{0ex}}\mathrm{tan}\theta =\frac{5}{9}\phantom{\rule{0ex}{0ex}}⇒\theta ={\mathrm{tan}}^{-1}\frac{5}{9}$Therefore, the raindrop will strike the windshield at an angle of ${\mathrm{tan}}^{-1}\frac{5}{9}$.

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