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.

Options

A. 125 h
B. 220 h
C. 432 h
D. 225 h

Answer

D

Explanation

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`