Answer:
Step-by-step explanation:
height of pole = 22 ft
height of girl = 5 ft
let the distance of girl from the foot to street light is x and the tip of shadow is at a distance from the street light.
dx / dt = 7 ft/s
By using the similarity of two triangles
[tex]\frac{y-x}{5}=\frac{y}{22}[/tex]
22 y - 22 x = 5 y
17 y = 22 x
[tex]y=\frac{22}{17}x[/tex]
Differentiate both sides with respect to t.
[tex]\frac{dy}{dt}=\frac{22}{17}\times \frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{22}{17}\times 7[/tex]
dy/dt = 9.06 ft/s
Thus, the tip of the shadow is moving with speed 9.06 ft /s.
