Question

four students are standing, one at each corner of a square of side 2m. They all start moving simultaneously, heading always towards the next one, with constant speed of 1 m/s. The time taken to meet is____

Answer 1

The motion of four persons K, L, M, N is as shown in figure by solid curved lines. They will be meeting at the centre O of the square KLMN. It means, that the person K will be covering a displacement KO befor meeting the other person.
Since each has same velocity, hence all will reach at point O at same time.
$$\begin{gathered} Sincetheyarecontinuouslymovingtowardseachotherandallofthemaremoving, \\ thetrajectoryoftheirmotionisasemi-circlewiththeendpointbeingthecentreofthe \\ squareanddiameterbeinghalfofthediagonal. \\ Dis\tan cemovedbyeachissameasaquarterofacirclei.e\pi r/2. \\ wherer=dis\tan ceofeachvertexofsquaretothecentre(wherediagonalsmeet)=d/\sqrt{2} \\ Timetaken=\frac{\pi d}{v2\sqrt{2}} \end{gathered}$$