Zombie apocalypse has started. You are at point A (3,2). At point B (−5,4) there is a shelter. A river flows along the X axis. You are running at a constant velocity 1 ms^(−1) with an intention to reach the shelter but before that, you have to reach the river and fill-up your water jar. What is the lowest time it takes to reach B from A? [It takes 1 second time to fill the jar with water.] a) 11.0 s b) 8.24 s c) 10.1 s d) 9 s


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Question Number 182405 by abdullah_ff last updated on 09/Dec/22

$Z o m b i e a p o c a l y p s e h a s s t a r t e d . Y o u$ $a r e a t p o i n t A (3, 2) . A t p o i n t B (- 5, 4)$ $t h e r e i s a s h e l t e r . A r i v e r f l o w s a l o n g$ $t h e X a x i s . Y o u a r e r u n n i n g a t a c o n s t a n t$ $v e l o c i t y 1 {m s}^{- 1} w i t h a n i n t e n t i o n t o$ $r e a c h t h e s h e l t e r b u t b e f o r e t h a t, y o u$ $h a v e t o r e a c h t h e r i v e r a n d f i l l - u p y o u r$ $w a t e r j a r . W h a t i s t h e l o w e s t t i m e i t$ $t a k e s t o r e a c h B f r o m A ? [I t t a k e s 1 s e c o n d$ $t i m e t o f i l l t h e j a r w i t h w a t e r .]$ $a) 11.0 s$ $b) 8.24 s$ $c) 10.1 s$ $d) 9 s$
Commented by mr W last updated on 09/Dec/22

$t h e q u e s t i o n w o u l d b e m o r e i n t e r e s t i n g,$ $w h e n y o u w i t h f i l l e d w a t e r j a r o n l y$ $r u n a t a s p e e d 0.6 {m s}^{- 1} .$
	Answered by CrispyXYZ last updated on 09/Dec/22

	$a$ $This question can be converted to :$ $A (3, 2), B (- 5, 4), P (p, 0)$ $Find t_{\min} = {(A P + B P + 1)}_{\min}$ $Algebra method :$ $A P = \sqrt{{(p - 3)}^{2} + 2^{2}}$ $B P = \sqrt{{(p + 5)}^{2} + 4^{2}}$ $t ⩾ \sqrt{{(p - 3 + p + 5)}^{2} + 6^{2}} + 1 = 11$ $t_{\min} = 11$
	Commented by CrispyXYZ last updated on 09/Dec/22

	Commented by abdullah_ff last updated on 09/Dec/22

	$t h a n k y o u$
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