You are caught without an umbrella in the rain and wish to g

You are caught without an umbrella in the rain and wish to get to your dorm ,1 km away, in the driest possible condition. Should you walk or run ? Calculate the rain drop collision with your body under two condition. Assume that the cross section is independent of direction and if you run at 8m/s and walk at 3 m/s rainfall is constant at velocity of 15m/s.

Solution

Answer:

Let N be the density of raindrops; and Z be the number of collisions/unit time between the man and the raindrops;

let V_walk and V_run be the man’s velocities for walking and running and D be the distance to the dorm (=1 km);

The number of collisions is given by Z, the number of collisions per unit time, times the time it takes to walk or run to the dorm, D/(V_walk or V_run )

  The number of collisions = ZD/ (V_walk or V_run )

So the wetness is ZD/(V_walk or V_run )

The no. of collisions per seconds for rain drop and walking man 3/15 of (collision frequency of rain drop and standing man \"X\")

The no. of collisions per seconds for rain drop and running man 8/15 of (collision frequency of rain drop and standing man \"X\")

The number of collisions (walking man)= (X/5)D/ (V_walk ) = X/15 =

The number of collisions (running man man) = (8/15) * X/ (V_run ) = 8X/225