Answer:
dy/dt= 0.6m/s
Explanation:
Ok, so we hace two right triangles ABC and ADE which are similar triangles, so we have their corresponding sides like:
[tex]\frac{AD}{AB}= \frac{DE}{BC}[/tex]
[tex]\frac{8}{12}= \frac{2}{Y}[/tex]
If we consider the distance of the man from the building as x then the distance from the spotlight to the man is 12-x
[tex]\frac{12-x}{12}= \frac{2}{y}[/tex]
[tex]1-\frac{1}{12}x= 2*\frac{1}{y}[/tex]
Now we have to take the derivatives of both sides
[tex]-\frac{1}{12}dx= -2*\frac{1}{y^2}dy[/tex]
We are now going to divide the hole equation by dt
[tex]\frac{dx}{dt}=1.6m/s^2[/tex]
[tex]\frac{-1}{12} \frac{dx}{dt} = -\frac{2}{y^2}\frac{dy}{dt}[/tex] and y=3
Let´s sustitute the data on the equation
[tex]-\frac{1}{12}*(1.6)= \frac{-2}{9}\frac{dy}{dt}[/tex]
So we have that
[tex]\frac{dy}{dt} =\frac{1.6}{12}*\frac{9}{2}=0.6m/s[/tex]
