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Home » 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, asexpected. (We are assuming there is no strong wind and that the rain falls verticallyfor a stationary man). Do you think this relation can be correct? If not, guess thecorrect relation.
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.
CBSE | Class 11 | NCERT | Physics | Units and Measurements
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.

Answer

The principle of homogeneity of dimensional equations states that the dimensions of L.H.S are equal to the dimensions of R.H.S.

In expression v = tan θ,

where tan θ is a trigonometric function and it is a dimensionless quantity.

But, the dimension of v = [L1 T-1]. Therefore, this relation is wrong.
To make the above relation correct, the left hand side should be divided by the velocity of rain, given by u.

Therefore, the expression becomes
v/u= tan θ

The above relation is correct dimensionally.

i

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