Question

a street light is at the top of a 18 ft tall pole.
a woman 6.5 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path.

how fast is the shadow lengthening when she is 30 ft from the base of the pole?
(round answers to 3 decimal places.)

\\(\text{ft}/\text{sec}\\)

how fast is the tip of her shadow moving when she is 30 ft from the base of the pole?
(round answers to 3 decimal places.)

\\(\text{ft}/\text{sec}\\)

Explanation:

Set up the geometric model

Using the Related Rates and Implicit Differentiation knowledge points

$$
LATEXBLOCK0
$$

Relate the variables

Using the Related Rates knowledge point

$$
LATEXBLOCK1
$$

Find the rate of shadow lengthening

Using the Related Rates and Implicit Differentiation knowledge points

$$
LATEXBLOCK2
$$

Find the rate of the shadow tip movement

Using the Related Rates knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

How fast is the shadow lengthening when she is 30 ft from the base of the pole?
(Round answers to 3 decimal places.)
<blank>3.391</blank> \(\frac{\text{ft}}{\text{sec}}\)

Question 2

How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?
(Round answers to 3 decimal places.)
<blank>9.391</blank> \(\frac{\text{ft}}{\text{sec}}\)