Answer:
0.6375 m/s
Explanation:
Let x be the distance of the man from the building
from the figure attached
initially the value of x=12
Given:
[tex]\frac{dx}{dt}=-1.7m/s[/tex]
where the negative sign depicts that the distance of the man from the building is decreasing.
Now, Let The length of the shadow be = y
we have to calculate [tex]\frac{dy}{dt}[/tex] when x=4
from the similar triangles
we have,
[tex]\frac{2}{12-x}=\frac{y}{12}[/tex]
or
[tex]y=\frac{24}{12-x}[/tex]
Differentiating with respect to time 't' we get
[tex]\frac{dy}{dt}=-\frac{24}{12-x}^2\frac{-dx}{dt}[/tex]
or
[tex]\frac{dy}{dt}=\frac{24}{12-x}^2\frac{dx}{dt}[/tex]
Now for x = 4, and [tex]\frac{dx}{dt}=-1.7m/s[/tex] we have,
[tex]\frac{dy}{dt}=\frac{24}{12-4}^2\times (-1.7)[/tex]
or
[tex]\frac{dy}{dt}=-0.6375m/s[/tex]
here, the negative sign depicts the decrease in length and in the question it is asked the decreasing rate thus, the answer is 0.6375m/s
