#3 Calculus Problem Help-Related Rates A man, who is 30 feet away from a 24 foot
ID: 2860849 • Letter: #
Question
#3 Calculus Problem Help-Related Rates
A man, who is 30 feet away from a 24 foot tall street lamp, is sinking into quicksand. (See diagram below.) At the moment when 4 feet of him is above the ground, his height above the ground is shrinking at a rate of 0.5 feet/second. How long will the man's shadow (shown in bold in the diagram above) be at the moment when 4 feet of him is above the ground? At what rate is the length of the man's shadow changing at the moment 4 feet of him is above the ground? Is his shadow growing or shrinking at that moment?Explanation / Answer
Sol :
Answer A:
In Given Triangle 4/x=24/30+x => x=6 thus answer to part a is that length of shadow when man's hieght is 6 ft.
Answer B:
we Know in smaller trinangle ( Hypertaneous )2=(Perpendicular)2+(Base )2
=> x2+y2= 42+62=52
2xdx+2ydy=0
dy = -(x/y)dx
dy=-(4/6)*(0.5)= -.33 => shadow is shrinking
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