Answer:
8.8ft/s
Step-by-step explanation:
Height of pole=11 foot
Height of man=6 foot
Let x be the distance of man from the pole and y be the distance of tip of shadow from the base of the pole.
[tex]\frac{dx}{dt}=4 ft/s[/tex]
Two right triangles are similar then the ratio of their corresponding sides are equal
[tex]\frac{6}{11}=\frac{y-x}{y}[/tex]
[tex]6y=11y-11x[/tex]
[tex]11x=11y-6y=5y[/tex]
Differentiate w.r.t t
[tex]11\frac{dx}{dt}=5\frac{dy}{dt}[/tex]
[tex]11\times 4=5\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{11\times 4}{5}=8.8ft/s[/tex]
Hence, the tip of her shadow is moving at the rate 8.8ft/s when she is 45 feet from the base of the pole
