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.

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Payal Gupta | Contributor-Level 10

8 months ago

This is a long answer type question as classified in NCERT Exemplar

Time require to avoid the collision T= l/v where l = mean free path =1/ $\sqrt[]{2} π d^{2} n$

Where n = N/V

n=number of aeroplanes/volume

= $\frac{10}{20 * 20 * 1.5} = 0.0167 k m$ ^-3

T= $\frac{1 V}{\sqrt[]{2} π d^{2} N} * \frac{1}{v}$

T= $\frac{1}{\sqrt[]{2} * 3.14 * 20^{2} * 0.0167 * 10^{- 6} * 150}$ = $\frac{10^{6}}{1776.25 * 2.505}$

$= \frac{10^{6}}{4449.5} = 224.74 h \approx 225 h$

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physics ncert solutions class 11th 2023

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