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 .

Mean free path

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Mean free path

Remember concepts with our Masterclasses.

Using kinetic theory of ideal gases,Mean collision time = t=mean free pathaverage velocity=λv=12πd2nv 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 .

Ready to Test Your Skills?

free study material