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. 250 h
B. 225 h
C. 330 h
D. 360 h

Answer

B

Explanation

Given , `v=150kmh^(-1)` ,`V=20xx20xx1.5km^(3)` , N = 10,`d=2xx10=20m`
time taken by plane ,
`t=lamda//V` and mean free path,
`lambda=(1)/(sqrt2pi^(2))n`
,where d= diameter and n = number of density
, So ,`n=(N)/(V)=(10)/(20xx20xx1.5)= 0.0167km^(-3)`
and time elapse between collision,
`t=(1)/(sqrt2d^(2)(N//V)xxv)`
`=(1)/(1.414xx3.14xx(20)^(2)(xx10^(-6))xx0.0167xx10^(-3)xx150)`
`t=225h`