Ten small planes are flying at a speed of `150 km//h` in total darkness in an air space that is `20 xx 20 xx 1.5 km^(3)` in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are, On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a safety region around the plane can be approximately by a sphere of radius 10 m.

Explanation

The situation can be considered as the time of relaxation based on kinetic theory of gases. Mean free path is the distance between two successive collision which we will consider here as the distance travelled by the plane before it just avoids the collision safe radius is equivalent to radius of the atom.
`t=l/v,l =` mean free path `=(1)/(sqrt(2) pi d^(2) n) n= " number density" =(N)/(V)`
`n= ("Number of aeroplanes(N)")/("Volume (v)")`
`=(10)/(20 xx 20 xx 1.5) =0.0167 Km^(-3)`
`t=(1)/(sqrt(2) pi d^(2) (N//V)) xx (1)/(V) " "[V = "Velocity of aeroplane"]`
By putting the given data,
`t=(1)/(sqrt(2) xx 314 xx (20)^(2) xx 0.0167 xx 10^(-6) xx 150)`
`=(10^(6))/(1776.25 xx 2.505)`
`=(10^(6))/(4449.5) =224. 74 h`
`~~ 225h`