Q29 of 31 Page 95

Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 × 20 × 1.5 km3 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 approximated by a sphere of radius 10m.

Given:


Speed of plane v=


diameter of safety region d=20m


No. of planes N=10


The average distance travelled by a plane between successive collisions can be find out by calculating the mean free path which is given by


…(i)


Where


n= no. of planes per unit volume



d=diameter of safety region


from eqn.(i)



Since


The time elapsed between two collisions can be given as




Putting all the values, we, get




The time elapsed between near collision with the plane is 225 hours.


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