(5 points) A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 6 ft/sec.
At what rate is the tip of her shadow moving away from the light (ie, away from the top of the
pole) when the girl is 22 ft away from the pole?

2.31 ft/sec

Step-by-step explanation:

In the picture attached, a representation of the problem is shown, where w(t) is the walking distance (as a function of time) and s(t) is the position of the tip of her shadow (as a function of time).

We want to find the derivative of s(t).

From triangles similarity:

s(t)/5 = [w(t) + s(t)]/18

18s(t) = 5w(t) + 5s(t)

13s(t) = 5w(t)

w(t) = 13/5*s(t)

We know that her speed is 6 ft/sec, that is:

d(w(t))/dt = 6 ft/sec

From the previous relationship:

d(w(t))/dt = 13/5*d(s(t))/t

Replacing:

6 = 13/5*d(s(t))/t

d(s(t))/t = 5*6/13

d(s(t))/t ≈ 2.31 ft/sec

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !