A man is moving downward on an inclined plane


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A man is moving downward on an inclined plane with a constant velocity v° and rain drops appear to him moving in horizontal direction with velocity 2v°. Please open the attached picture for further details.

Answered by admin @



This question is based on relative concepts of rain and main.
Let \bf{v_{mg}= v_m}is relative velocity of man with respect to ground.
\bf{v_{rg}=v_r} is the relative velocity of rain with respect to ground.
And \bf{v_{rm}} is the relative velocity of rain with respect to man.
Relation between \bf{v_m,v_r\:and\:v_{rm}} is \bf{v_{rm}=v_r-v_m} 

Given,
\bf{v_m}= v₀cos37°(-i) + v₀sin37°(j) 
\bf{v_m} = -4v₀/5 i + 3v₀/5 j 
and \bf{v_{rm}} = 2v₀ i 
Hence, \bf{v_{rm}=v_r-v_m}
\bf{v_r} =2v₀i +(-4v₀/5 i + 3v₀/5 j) 
= 6v₀/5 i + 3v₀/5 j ----(1)

Now, velocity of man with respect to ground, \bf{v_m}​ = -2v₀cos37° i + 2v₀sin37°j 
= -8v₀/5 i + 6v₀/5 j 
\bf{v_{rm}}​ = 6v₀/5 i + 3v₀/5 j -(- 8v₀/5 i + 6v₀/5 j)
= 14v₀/5 i - 3v₀/5 j
Now, |\bf{v_{rm}} | = √{(196 + 9)/25}v₀ = √{205/25}v₀ =√(41/5)v₀
Hence, n =41

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