Four-particles-A-B-C-and-D-are-situated-at-the-corners-of-a-square-ABCD-of-side-a-at-t-0-Each-of-the-particles-moves-with-constant-speed-v-A-always-has-its-velocity-along-AB-B-along-BC-C-along

Question Number 13449 by Tinkutara last updated on 20/May/17

Four particles A, B, C and D are situated

at the corners of a square A B C D of side

a at t = 0 . Each of the particles moves

with constant speed v . A always has its

velocity along A B, B along B C, C along

C D and D along D A . At what time will

these particles meet each other ?

Answered by mrW1 last updated on 20/May/17

W h e n t h e p a r t i c l e s m o v e, t h e d i s t a n c e

b e t w e e n t h e m w i l l b e r e d u c e d f r o m a

t o 0 w i t h t h e s p e e d v . T h e t i m e t h e y

n e e d i s

t = \frac{a}{v}

Commented by Tinkutara last updated on 20/May/17

But can you explain why they will meet ?

Since they all are moving with constant

speeds in the same direction along the

sides of a square, they should never

meet .

Commented by ajfour last updated on 20/May/17

t h i s i s s i m p l e a n d g o o d .

Commented by ajfour last updated on 20/May/17

t h e s q u a r e A B C D r e m a i n s a

s q u a r e b u t d e c r e a s e s i n e d g e l e n g t h

a n d t u r n s a b o u t i t s c e n t r e w h e r e

t h e v e r t i c e s c o m e t o g e t h e r, i n a

t i m e r e q u i r e d f o r t h e e d g e l e n g t h

t o v a n i s h, a t a r a t e = v .

h e n c e t = a / v .

Commented by mrW1 last updated on 20/May/17

T h e t r a c k o f e a c h p a r t i c l e i s c u r v e w h i c h

h a s t h e l e n g t h a . A t e v e r y t i m e t h e

p o s i t i o n o f t h e p a r t i c l e s i s a s q u a r

w h i c h r o t a t e s a n d g e t s s m a l l e r a n d

s m a l l e r t i l l a s i n g l e p o i n t .

Commented by mrW1 last updated on 20/May/17

Commented by Tinkutara last updated on 20/May/17

Thanks to both mrW 1 and ajfour .

Commented by mrW1 last updated on 20/May/17

I f o u n d s o m e p i c t u r e s i n I n t e r n e t

Commented by mrW1 last updated on 20/May/17

Commented by mrW1 last updated on 20/May/17

Answered by ajfour last updated on 20/May/17

c o m p o n e n t o f v e l o c i t y t o w a r d s

c e n t r e = \frac{v}{\sqrt{2}}

d i s t a n c e t o c e n t r e = \frac{a}{\sqrt{2}}

t h e y w i l l m e e t a t t h e c e n t r e

i n a t i m e t = \frac{(a / \sqrt{2})}{(v / \sqrt{2})} = \frac{v}{a} .

Commented by ajfour last updated on 20/May/17

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