Answer: [tex]\frac{8}{3}\ ft/s[/tex]
Step-by-step explanation:
Given
length of shadow =22 ft
height of woman =5.5 ft
speed of woman [tex]\frac{dy}{dt}=8\ ft/s[/tex]
from the figure, we can write
[tex]\frac{22}{x+y}=\frac{5.5}{x}[/tex]
at given instant
y=20 ft
so, using similar triangle properties
[tex]\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft[/tex]
Again we can write
[tex]\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}[/tex]
