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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Four Mice Problem

At t = 0, four particles A, B, C and D are situated at the vertices of a square ABCD of side d. Each particle moves with constant speed v such that A always has its velocity along AB, B along BC, C along CD and D along DA. At what time will the particles meet?

Solution

Let us consider particles A and B.

The relative velocity of B w.r.t. A can be obtained from the right triangle formed by the two velocity vectors:

$v_{rel}=\sqrt 2 .v$

The component of $v_{rel}$ along BA = $v_{rel} cos45^\circ $ = v

This component will decrease the distance d.

So, $t=\frac {d}{v}$