Answer:
The length of shadow decrease at 0.48 m/s.
Step-by-step explanation:
The distance of man from building = x
Thus initially, x = 12
It is given that dx/dt= -1.3 m/s
Let the shadow height = Y
Now solve for the [tex]dy/dt[/tex] when x=4
from the diagram (triangle) it can be seen similar triangles with similar base/height ratios.
[tex]\frac{2}{12-x} = \frac{y}{12} \\Y = \frac{24}{12 - x} \\ \frac{dy}{dt} = \frac{24}{(12-x)^{2}} \times \frac{dx}{dt} \\at x=4, dy/dt \ becomes: \\\frac{24}{(12-4)^2} \times -1.3 \\= -0.48 m/s[/tex]
