Posted by Anonymous on Tuesday, October 23, 2012 at 4:47pm.
Make the diagram. The streetlight height is 16. Let the distance from the streetlamp base to the tip of the shadow as x. Label the distance from the streetlamp base to the person as d.
Similar triangles:
16/x=5/(x-d)
5x=16x-16d
11x=16d
11 dx/dt=16 dd/dt
dd/dt =5.5ft/sec, solve for dx/dt
I do not agree with bobpursley's solution
let the distance of the woman from the streetlight be x ft
let the length of her shadow be y ft
by ratios ...
5/y = 16/(x+y)
16y = 5x + 5y
11y = 5x
11 dy/dt = 5 dx/dt
but dx/dt = 5.5
dy/dt = (5/11)(5.5) = 2.5
So her shadow is lengthening at 2.5 ft/sec
but she is moving at 5.5 ft/sec, so her shadow is moving at 2.5+5.5 or 8 ft/sec
( I am walking along the inside of a moving train at 3 ft/sec, while the train is moving at 50 ft/sec
So I am moving at 53 ft/sec)
Reiny is definitely correct.
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