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virtus
 3 years ago
A 6m high vertical street lamp stands on horizontal ground. A 2 metre tall man runs away from the street lamp at a constant speed of 2.5m/s. When he is y metres from the street lamp his shadow has length x metres.
Find the rate at which his shadow lengthens
virtus
 3 years ago
A 6m high vertical street lamp stands on horizontal ground. A 2 metre tall man runs away from the street lamp at a constant speed of 2.5m/s. When he is y metres from the street lamp his shadow has length x metres. Find the rate at which his shadow lengthens

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timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3keep the light as the origin is 0

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3and the ground as zero also

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3there fore slope for the hypotonuse form is dy/dx (62) = dy which is fixed i think so 4 4/(02*x)

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3sfx x = 3.75*x1 by x i mean x+y 3.75*x1=2.5x1+unkn unkn = 6.25*x1

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3dw:1342238127714:dw another way to look at it

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3where m1= (64)/(2.5x) and m2=  6/ (2.5x+b) set them equal to eachothter find b

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.3b=5x so s a b 1 2.5 5 2 5 10 3 7.5 15 It looks like everysecond the shadow gets 5 meters longer so it is a constant growth of 5 m/s i think

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.0From the figure,\[\frac{y+x}{6}=\frac{x}{2} \]The Total Derivative of the above equation is:\[\frac{1}{6} (dx+dy)=\frac{dx}{2} \]Solve for dx:\[dx=\frac{dy}{2} \]Replace dy with 2.5 and simplify.\[dx=1.25 m/\sec \]
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