A street light is at the top of a 16 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 35 ft from the base of the pole?

Answer 1

The tip of the shadow is moving at #4.8 "ft"/"sec"#

Consider the situation as depicted in the image below:#rarrcolor(white)("XXXX")10s(t) = 6w(t)#

#rarrcolor(white)("XXXX")w(t) = 10/6s(t)#

We are told that a a certain time #t#
#color(white)("XXXX")(d(w(t)))/(dt) = 8 "feet"/"second"#

#(d(w(t)))/(dt) = (d(10/6s(t)))/(dt)#

#color(white)("XXXX")= 10/6(d(s(t)))/(dt)#

Therefore
#color(white)("XXXX")10/6 (d(s(t)))/(dt) = 8 "feet"/"second"#

#rarrcolor(white)("XXXX")(d(s(t)))/(dt) = 4.8 "feet"/"second"#

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Answer 2

The tip of her shadow is moving at ( \frac{64}{5} ) ft/sec.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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