Four-persons-a-b-c-d-are-standing-at-four-vertices-of-square-ABCD-All-four-start-moving-simultaneously-such-a-is-always-moving-towards-b-on-a-straight-line-between-a-and-b-Similary-b-is-always-mo

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Question Number 4140 by prakash jain last updated on 29/Dec/15

$$\mathrm{Four}\mathrm{persons}\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\mathrm{are}\mathrm{standing}\mathrm{at}\mathrm{four}$$$$\mathrm{vertices}\mathrm{of}\mathrm{square}\mathrm{ABCD}.$$$$\mathrm{All}\mathrm{four}\mathrm{start}\mathrm{moving}\mathrm{simultaneously}\mathrm{such}$$$$\mathbf{a}\mathrm{is}\mathrm{always}\mathrm{moving}\mathrm{towards}\mathbf{b}\mathrm{on}\mathrm{a}\mathrm{straight}$$$$\mathrm{line}\mathrm{between}\mathbf{a}\mathrm{and}\mathbf{b}.\mathrm{Similary}\mathbf{b}\mathrm{is}\mathrm{always}$$$$\mathrm{moving}\mathrm{directly}\mathrm{towards}\mathbf{c},\mathbf{c}\mathrm{is}\mathrm{directly}$$$$\mathrm{moving}\mathrm{towards}\mathbf{d}\mathrm{and}\mathbf{d}\mathrm{is}\mathrm{directly}\mathrm{moving}$$$$\mathrm{towards}\mathbf{a}.$$$$\mathrm{Do}\mathrm{they}\mathrm{all}\mathrm{meet}?\mathrm{How}\mathrm{much}\mathrm{will}\mathrm{be}\mathrm{the}$$$$\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{each}\mathrm{when}\mathrm{they}\mathrm{meet}?$$

Commented by prakash jain last updated on 30/Dec/15

$$yes.$$

Commented by Rasheed Soomro last updated on 30/Dec/15

$$\mathrm{If}\mathrm{all}\mathrm{are}\mathrm{moving}\mathrm{contineously},\mathrm{their}\mathrm{direction}$$$$\mathrm{of}\mathrm{movement}\mathrm{should}\mathrm{change}\mathrm{at}\mathrm{every}\mathrm{point}.$$$$\mathrm{That}\mathrm{means}\mathrm{they}\mathrm{are}\mathrm{moving}\mathrm{along}\mathrm{curved}$$$$\mathrm{path}.$$$$\mathrm{Their}\mathrm{movements}\mathrm{for}\mathrm{short}\mathrm{time}\mathrm{interval}\delta \mathrm{t}$$$$\mathrm{can}\mathrm{be}\mathrm{cosidered}\mathrm{in}\mathrm{straight}\mathrm{line}.\mathrm{If}\mathrm{I}\mathrm{have}$$$$\mathrm{understood}\dots .$$

Commented by Rasheed Soomro last updated on 31/Dec/15

$$\bullet \mathbf{T}\mathrm{hey}\mathrm{will}\mathrm{meet}\mathrm{at}\mathrm{the}\mathrm{center}\mathrm{of}\mathrm{the}\mathrm{square}.$$$$\bullet \mathrm{When}\mathrm{they}\mathrm{will}\mathrm{meet},\mathrm{they}\mathrm{will}\mathrm{be}\mathrm{at}\mathrm{the}$$$$\mathrm{distance}\mathrm{equal}\mathrm{to}\mathrm{half}\mathrm{of}\mathrm{the}\mathrm{diagonal}\mathrm{of}\mathrm{the}$$$$\mathrm{square},\mathrm{from}\mathrm{their}\mathrm{original}\mathrm{positions}.$$

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