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Question Number 108175 by bemath last updated on 15/Aug/20

Commented by bemath last updated on 15/Aug/20

$a m a n 6 f e e t t a l l w a l k s a t a r a t e 6 f e e t$ $p e r s e c o n d a w a y f r o m a l i g h t t h a t$ $i s 15 f e e t a b o v e t h e g r o u n d .$ $W h e n h e i s 10 f e e t f r o m t h e b a s e o f t h e l i g h t$ $a t w h a t r a t e i s t h e t i p o f h i s s h a d o w$ $m o v i n g ?$
Commented by john santu last updated on 15/Aug/20

Commented by john santu last updated on 15/Aug/20

$\frac{s_{1}}{s_{1} + s_{2}} = \frac{6}{15} \Rightarrow \frac{s_{1}}{10 + s_{1}} = \frac{2}{5}$ $5 s_{1} = 20 + 2 s_{1} \Rightarrow s_{1} = \frac{20}{3} f e e t$ $v = \frac{s_{1} + s_{2}}{t} = \frac{10 + \frac{20}{3}}{(\frac{5}{3})} = \frac{50}{5} = 10 f e e t / s e c o n d$
	Answered by mr W last updated on 15/Aug/20

	$x = p o s i t i o n o f t h e m a n$ $s = p o s i s t i o n o f t h e t i p o f t h e s h a d o w$ $l = l e n g t h o f t h e s h a d o w$ $\frac{s - x}{6} = \frac{s}{15}$ $\Rightarrow s = \frac{5}{3} x$ $l = s - x = \frac{2}{3} x$ $\frac{d s}{d t} = \frac{5}{3} \times \frac{d x}{d t} = \frac{5}{3} \times 6 = 10 f t / s e c$ $\frac{d l}{d t} = \frac{2}{3} \times \frac{d x}{d t} = \frac{2}{3} \times 6 = 4 f t / s e c$
	Commented by bemath last updated on 15/Aug/20

	$t h a n k y o u m r W$
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