Answer:
the rate of the change of the length of the shadow is - 0.8625 m/s.
The negative(-) sign means the length of the shadow decreases at a rate of 0.8625 m/s.
Explanation:
Given the data in the question;
Let x represent the man's distance from building,
initially x = 1m2
dx/d t= -2.3 m/s
Also Let y represent shadow height
so we determine dy/dt when x is 4m from the building
form the image description of the problem, we see two-like triangles with the same base and height ratios
so
2 / (12-x) = y / 12
24 = y(12 - x )
y = 24 / (12-x)
dy/dt = 24/(12-x)² × dx/dt
Now at x = 4,
we substitute
dy/dt will be;
⇒ 24/(12 - 4)² × -2.3
= 24/64 - 2.3
= 0.375 × -2.3
dy/dt = - 0.8625 m/s
Therefore, the rate of the change of the length of the shadow is - 0.8625 m/s.
The negative(-) sign means the length of the shadow decreases at a rate of 0.8625 m/s.
