Question

An ant starts from A and reaches F. In doing so it travels along path that is S shaped. If each side of the transversed path is same then Find the ratio of distance covered by the ant to the displacement.​

Answer 1

Answer :

Hey there mate here is your answer,

Let us take AB = BC = CD = DE = EF = x

Distance travelled by the ant = AB + BC + CD + DE + EF

                                                = x + x + x + x + x

                                                = 5x

Displacement is the shortest distance from initial to final point (A - F)

By Pythagoras Theorem,

$AF^{2} = (AD+DE)^{2} + FE^{2}\\AF^{2} = (BC+DE)^{2} + FE^{2}\\AF^{2} = (x+x)^{2} + x^{2}\\AF^2 = 2x^{2} + x^{2}\\AF^2 = 3x^{2}\\AF = \sqrt{3x^{2}}\\AF = \sqrt{3}x$  

Displacement of ant = $\sqrt{3}x$

Ratio of distance to displacement = 5x : $\sqrt{3}x$

                                                        = √5 : 1

THANKS …..