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Question

A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

Answer 1

street light is 12 feet high

woman is 6 feet tall, moving away at a speed of 8 ft/sec

when she's 50 feet from the pole, how fast is the tip of her shadow moving??

construct similar right triangles

s/12 = 50/6

s =100 feet

h^2 = s^2 + a^2

take derivatives

2hh' = 2ss' + 2aa' divide by 2

hh' = ss' + aa' where s=100, a =6, a'=0,

speed of shadow's tip is 16 feet per second, twice her speed

and is independent of how far away she is