two parallel paths 26m apart run east−west through the woods. one person east on one path at 3 kmph and another west on other path at 4 kmph. if they pass each other at time t =0 , i)how far apart are they 8 sec later? ii) how fast is the distance between them changing at that mlment? iii)find the distance L between them at 8 sec and (dL/dt)?


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Question Number 157739 by gsk2684 last updated on 27/Oct/21

$t w o p a r a l l e l p a t h s 26 m a p a r t r u n$ $e a s t - w e s t t h r o u g h t h e w o o d s .$ $o n e p e r s o n e a s t o n o n e p a t h a t$ $3 k m p h a n d a n o t h e r w e s t o n o t h e r$ $p a t h a t 4 k m p h . i f t h e y p a s s e a c h$ $o t h e r a t t i m e t = 0,$ $i) h o w f a r a p a r t a r e t h e y$ $8 s e c l a t e r ?$ $i i) h o w f a s t i s t h e$ $d i s t a n c e b e t w e e n t h e m c h a n g i n g$ $a t t h a t m l m e n t ?$ $i i i) f i n d t h e d i s t a n c e L$ $b e t w e e n t h e m a t 8 s e c a n d \frac{d L}{d t} ?$
Commented by gsk2684 last updated on 27/Oct/21

$c o u l d y o u p l s a n s w e r t h i s .$
	Answered by Kunal12588 last updated on 27/Oct/21

	$a t i m e = t$ $p o s i t i o n o f f i r s t p e r s o n = 3 t \hat{i}$ $p o s i t i o n o f s e c o n d p e r s o n = - 4 t \hat{i}$ $d i s t a n c e b e t w e e n t h e m = ∣ 3 t - (- 4 t) ∣= 7 t$ $(a s s u m i n g^{'} t^{'} i s p o s i t i v e)$ $(i) a t t = 8$ $d i s t a n c e b e t w e e n t h e m = 7 \times 8 = 56 k m$ $(i i) \frac{d}{d t} (7 t) = 7 k m p h . i r r e s p e c t i v e o f t h e t i m e$ $(i i i) L = 56 k m a n d \frac{d L}{d t} = 7 k m p h$
	Commented by gsk2684 last updated on 28/Oct/21

	$t h a n k s$ $a n d i t i s g u v e n t h a t t h e p a t h s a r e$ $p a r a l l e l n o t o n t h e s a m e l i n e .$ $a n d t h e y a p a r t 26 m .$
	Commented by Kunal12588 last updated on 29/Oct/21

	Commented by gsk2684 last updated on 30/Oct/21

	$t h a n k s (° ⌣ °)$
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