Question
A man walking briskly in rain with speed v must slant his umbrella forward making an angle 
with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit : as v →0, θ → 0 as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man.) Do you think this relation can be correct? If not, guess the correct relation.
with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit : as v →0, θ → 0 as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man.) Do you think this relation can be correct? If not, guess the correct relation. Solution
The relation tan 
= v is wrong because the dimensions on both the sides of the equation are not equal.
Dimension of right hand side is [MoL1T-1]
Dimension of Left hand side quantity is [MoLoTo]
Hence, the equation is wrong.
To make the relation dimensionally correct, R.H.S should be divided by the speed of the rainfall.
That is,
, is a dimensionally correct relation.
= v is wrong because the dimensions on both the sides of the equation are not equal.Dimension of right hand side is [MoL1T-1]
Dimension of Left hand side quantity is [MoLoTo]
Hence, the equation is wrong.
To make the relation dimensionally correct, R.H.S should be divided by the speed of the rainfall.
That is,
, is a dimensionally correct relation. 
