Let’s assume you are stuck in the rain and want to get
minimum wet then is it better run or walk or stand in the same place? Well
let’s not fret about this question and do some math in arriving at the answer.
Before we go ahead and solve this complex question let us make certain
assumptions such as no friction and other wind constraints and also another
assumption that the direction and speed of rain remain the same with space and
time.
First let’s assume we are stuck in a meadow with no shelter
nearby. Let’s represent the velocity of the rain as Vr. It has a
vertical component (Vr2) pointing downwards and horizontal component
(Vr1). The rain hits the person both from the top as well as
sideways.
If the rain is
unlikely to stop and we have no shelter nearby then it is of no use running
because the rain striking from the top remains same. Also if the person moves
sideways then there is a chance that the person will be hit by more rain drops
than standing still. So it is considered to be of no use to run in rain if the
person doesn’t have a shelter nearby.
It is very unlikely in today’s world that the person stands
in a meadow with no shelter nearby, so let’s see what to do if we are stuck in
the rain with a shelter nearby and the rain is unlikely to stop before reaching
the shelter. It is of no use to stand in the rain when we can reach the nearby
shelter in lesser time.
From the above two points it is observed that the wetness
due to vertical component of rain depends only on the time for which the person
stays in rain and the wetness due to horizontal component depends on the
distance from the shelter.
Therefore it can be written as
Wetness(top) α Vr2 X time spent in the rain ---(1)
Also
Wetness(side) α Vr1X
distance
travelled ---(2)
Thus the total wetness α (Vr2 X time spent
in the rain)+ (Vr1X distance
travelled) ---(3)
We need to minimize the total wetness in order to arrive at the
optimum speed.
The distance travelled remains constant as we ll be approaching
the nearest shelter. Hence it is important to minimize the only variable which
is the time spent in the rain. As the time spent in the rain is inversely
proportional to the speed, it is suggested to increase the speed as much as
possible to minimize the wetness. Hence it is suggested to run as quickly as
possible if a shelter is found nearby !!!
