Question

A woman 5 ft tall walks at the rate of 7.5 ft/sec away from a streetlight that is 10 ft above the ground. At what rate is the tip of her shadow moving? At what rate is her shadow lengthening?

Answer 1

angle with horizontal to top of pole =
\[ \tan^{-1}(\frac{poleHeight}{current position})\]

distance from pole to tip of shadow =
\[\frac{poleHeight}{\tan(\angle horz)}\]

current shadow length = tip of shadow - current position

rate of shadow increase =\[\frac{d}{dx} currentShadowLength\]
x being current position of the person


rate that the tip is moving is\[\frac{d}{dx} distanceFrmoPoleToTipOfShadow\]
x also being current position

Answer 2

Your explanation is confusing to me..

Answer 3

have you learned derivatives?

Answer 4

yes

Answer 5

so what part is confusing?

Answer 6

how to find the solution

Answer 7

follow the steps i just gave you, it's a series of equations you need to put together