(5 points) A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path
1 answer:
Answer:
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
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