### Question 2.25

NCERT Class XI Physics

A man walking briskly in rain with speed v must slant his umbrella forward making an angle θ 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 given relation is $\displaystyle \tan \theta = v$

Dimensions on LHS are $\displaystyle [\tan \theta ] \equiv [M^0L^0T^0]$

Dimensions on RHS are $\displaystyle [v] \equiv [M^0L^1T^{-1}]$

The dimensions are not same so formula cannot be correct.

If dimensions of speed are multiplied on the LHS, then the formula can become dimensionally correct.

So the guess is $\displaystyle u \tan \theta = v$, where $\displaystyle u$ is the vertical speed of the falling rain !

### Video Explanation

Please watch this youtube video for a quick explanation of the solution:

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