Ten small planes are flying at a speed of $$150kmph$$ in total darkness in an air space that is $$20$$×$$20$$×$$1.5km3$$ 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 an average, about $$25$$×N hours time will elapse between collision of a plane with your plane. Assume a safety region as a sphere of radius $$10$$ m around every plane. Find N.

Question

Ten small planes are flying at a speed of $$150kmph$$ in total darkness in an air space that  is  $$20$$×$$20$$×$$1.5km3$$ 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 an average, about  $$25$$×N  hours time will elapse between collision of a plane with your plane. Assume a  safety region as a sphere of radius $$10$$ m around every plane. Find N.

Infinity Learn · Accepted Answer

Using kinetic theory of ideal gases,Mean collision time $$=$$ $$t=mean$$  free  pathaverage  $$velocity=$$λ$$v=12$$$$π$$$$d2nv$$ Where, n $$=$$ number density of planes and d $$=$$ $$safe-region$$ $$diameter=2R=2(10)m=20m=20$$×$$10-3kmHere$$,  $$n=number$$  of  $$planesvolume=1020$$×$$20$$×$$1.5km3=0.0167$$  km−$$3$$⇒$$t=12$$×$$3.14$$×$$202$$×$$10$$−$$60.0167$$×$$150=225$$  h .

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!