Answer:
20/3 ft/sec
Step-by-step explanation:
As given the diagram (attached),
x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole.
I assume that the man and the pole are upright, meaning the 2 triangles are identical.
By similar triangles, we will get
15/y = 6/(y-x)
Triangles are similar if they have the same shape, but can be different sizes. In our case, triangles are in similar shape but in different sizes
15 (y-x) = 6y
15y-15x=6y
9y=15x
y=5/3 x
As we need to find rate of change (How fast), differentiate both sides with respect to time t. we get
dy/dt = 5/3 dx/dt
As we have given that the man is walking from the with a speed to 4ft/s
so dx/dt = 4, So, we need to find dy/dt (How fast the tip of shadow moving)
dy/dt = 5/3 *4
dy/dt = 20/3 or 6.666 ft/sec
In this case, the man's distance from the pole doesn't matter, because only his velocity influences how quickly his shadow goes.
