A man 6 ft tall walks at a

Answered question

2022-04-08

A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 12 ft high. At what rate is the length of his shadow changing when he is 25 ft away from the lamppost?

Answer & Explanation

nick1337

nick1337

Expert2022-06-08Added 777 answers

Let x be the distance between the man and the street light and let y be the length of his shadow. Note that we have two similar right triangles OLM and OAB. Hence using the similar triangle property, we get

5y=12x+y

5(x+y)=12y

5x=12-5y

y=57x

Differentiating with respect to time t partially, we get

dydt=57dxdt

Now Since the man is walking away's from the lamp at a rate ot 5 ft/s.

dxdt=5

Hence at the moment when he is 25 ft aways from the lamppOst, the length of his shadow is changing at a rate of

dydt=57*5=257 ft/s3.6 ft/s

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