Rain Rain come back another day
When a man moves down the inclined plain with constant speed 5 which makes an angle of with the horizontal, he finds that the rain is falling vertically downward. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle = with the horizontal. The speed of the rain (w.r.t man) can be expressed as .
Give your answer as
The answer is 20.0000.
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1 solution
In order to obtain the correct solution of 20 I had to make a couple of guesses as to the exact meaning of the question. Firstly in order to obtain the answer in a surd form, it is never going to coming from a slope of precisely 37 o . So I reckoned that 37 o was another way of saying the slope was arctan(3/4), (the difference is less than 0.2%).
Since the man experiences the rain as falling vertically downwards the horizontal component of the rain's velocity must equal the man's, i.e. 4 m/s (horizontally in the downslope direction).
When the man is moving up the slope the he experiences the horizontal component of their relative velocity as 8 m/s. Since the rain appears to him to become at an angle of arctan(7/8), the relative vertical component must be 7m/s. However the man is ascending at 3 m/s vertically so the rain is actually descending at 4 m/s.
Now the question asks what is the speed of the rain (w.r.t man), but it does not say what the man is doing, going up, down or stopped.
Going up is leads to 8 2 + 7 2 implying a=1, b=113
Going down leads to 1 implying a=1, b=1
If the man is stationary we get 4 2 + 4 2 = 4 2 giving a=4,b=2 and the required answer of 20.
At a technical level this is not at level 5 mechanics, except for the obfuscations in the question, perhaps making it so.