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A street light is on top of a 9 foot pole. Joe, who is 3 feet tall, walks away from the pole at a rate of 4 feet per second. At what speed is the tip of Joe’s shadow moving from the base of the pole when he is 10 feet from the pole?

Respuesta :

Answer:2 ft/s

Explanation:

Given

Length of Pole is 9 ft

Length of Joe is 3 ft

Joe walks away from Pole at the rate 4 ft/s

Let Joe is x m away from Pole so its shadow length is x'

From Similar triangle concept

[tex]\frac{x'}{x+x'}=\frac{3}{9}[/tex]

3x'=x+x'

x=2x'

and it is given [tex]\frac{\mathrm{d} x}{\mathrm{d} t}=4 ft/s[/tex]

Differentiating

[tex]\frac{\mathrm{d} x}{\mathrm{d} t}=2\frac{\mathrm{d} x'}{\mathrm{d} t}[/tex]

[tex]4=2\times \frac{\mathrm{d} x'}{\mathrm{d} t}[/tex]

[tex]\frac{\mathrm{d} x'}{\mathrm{d} t}=2 ft/s[/tex]

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