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.

Ten small planes are flying at a speed of 150 km//h in total darkness

1.	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.
Answer» 125 h 220 h 432 h 225 h Solution :Here, `v=150Kmh^(-1)N=10` `V=20xx20xx1.2Km^(3).` Dimeter of plane, `d=2R=2xx10` `= 20 m 20xx10^(-3)km` `n=N/V=(10)/(20xx20xx1.5)=0.067Km^(-3)` Mean free path of a plane `lamda =(1)/(sqrt2pid^(2)n)` Time elapse before collision of TWO planes randomaly, `t=(lamda)/(v)=(1)/(sqrt2pid^(2)NV)` `=(1)/(1.414xx3.14xx(20)^(2)xx10^(-6)xx(0.0167)xx(150))` `=(10^(6))/(4449.5)=224.74h~~225h`