This man is crazy

Classical Mechanics Level 5

Figure above depicts a situation when it's raining (as shown by arrows) and the man is moving on the track. Find the actual speed of the rain in m/s \text{m/s} .


The answer is 5.77.

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

While going down, rain is in the direction of his motion which is at 30 degrees to horizontal.
While moving up, he is at 60 degrees, rain at 30 degrees, and apparent, relative to him rain at 90 degrees.
So in a 30-60-90 right angled triangle, he is at 10 m/s leg, at 30 degrees with vertical hypotenuse.
So the other shorter leg at 60 to hypotenuse is 10 3 = \hgue 5.77350. \dfrac {10}{\sqrt3}=\hgue\ \ \ \ \color{#D61F06}{5.77350.}\\
Checking on st. track confirms this.


1 Helpful 0 Interesting 0 Brilliant 0 Confused

Sir, will this do?

On the horizontal stretch, man's speed 5m/s must have balance horizontal component of the rain, because it appears vertical. So the horizontal component of the rain is 5m/s.

While going down the 30° incline rain appears parallel to the incline. So slowing down or speeding up will change only the relative magnitude but not the relative direction. So the actual direction of the rain must be at 30° with the horizontal.

Now if the horizontal component is 5 m/s, the rain speed must be 5 cos ⁡ 30 = 10 3 \frac{5}{\cos 30} = \frac{10}{\sqrt{3}}

Ujjwal Rane - 4 years, 11 months ago

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