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

Time between near collision `t =(lambda)/(upsilon)` where `lambda` is mean free path = `(1)/(sqrt(2)pi n d^(2))`
where d is diameter of safety region = `20 m = 20 xx 10^(-3) km`
and n=number density ` N/V = (10)/(20 xx 20 xx1.5) = 0.0167 km^(-3)`
we are given `upsilon=150 km//h`
As `t = (lambda)/(upsilon) :. t = (1)/([sqrt(2) pi nd^(2)]upsilon) = 1/(1.414 xx 3.14 xx 0.0167 xx (20xx10^(-3))^(2) xx 150) = 225 hour`.