Chapter 3, Problem 20Q

Solution

To Determine:

To Explain: If one starts running in rain which is falling vertically, the rain begins to hit one’s legs even if one remains under the umbrella.

Solution:

The velocityof raindrops with respect to moving man is inclined at some angle with the vertical, so raindrops hit the legs of the man.

Explanation:

Given:

The velocity of rain with respect to ground is vertically downwards.

Formula Used:

The relative velocity can be obtained by:

  $\begin{array}{l}{\overrightarrow{V}}_{R,M}={\overrightarrow{V}}_{RG}+{\overrightarrow{V}}_{GM}\\ {\overrightarrow{V}}_{R,M}={\overrightarrow{V}}_{RG}-{\overrightarrow{V}}_{MG}\end{array}$

Where, ${\overrightarrow{V}}_{R,M}$ is the velocity of the rain with respect to man, ${\overrightarrow{V}}_{RG}$ is the velocity of rain with respect to the ground, ${\overrightarrow{V}}_{MG}$ is the velocity of man with respect to the ground.

Explanation:

When the man is motion less, the relative velocity of rain with respect to man would be:

  ${\overrightarrow{V}}_{R,M}=\left({\overrightarrow{V}}_{RG}\right)$

When the man starts moving, the relative velocity of the rain with respect to man would be:

  ${\overrightarrow{V}}_{R,M}=\left({\overrightarrow{V}}_{RG}\right)+\left(-{\overrightarrow{V}}_{MG}\right)$

One can infer that as the man starts moving, the raindropsfall inclined at some angle.So even if the man has an umbrella, the raindrops hit his legs.