A street light is mounted at the top of a 15 foot-tall pole. A man 6ft tall walks away from the pole with the speed of 5ft/s along a straight path. How fast is the tip of his shadow moving when he is 40ft from the pole?

Question

anonymous · Answer

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man pole
Let x be the distance between the man and the pole.
dx/dt=5
Let y be the distance between the man and the tip of his shadow (length of the shadow)
Let x+y = z (the distance between the tip of the shadow and the pole)
By using similar triangles,
z/15 =x / (15-6)
z/15 = x/9
z=(15/9) x
z=(5/3)x
dz/dt = (5/3) dx/dt
dz/dt = (5/3)(5)=25/3=8 1/3
Regardless of how far he is from the pole, the tip of his shadow is moving at a rate of 8 1/3 ft /s

anonymous · Answer

Hope this was helpful, give me medal.

anonymous · Answer

i don't get it

phi · Answer

|dw:1352567783516:dw|

phi · Answer

I think that is how blast set it up, using similar triangles.

phi · Answer

if you get that far, the calculus is pretty straight-forward.
15 x = 9 s
15 dx/dt =9 ds/dt
or 
ds/dt = 5/3  dx/dt

phi · Answer

I am not sure how you figure this out, but the top triangle with base leg x  is moving at 5 ft/sec.  Meanwhile, the base leg s is moving at ds/dt (it is growing faster than 5 ft/sec because the shadow is growing longer...)