Since only the man's speed influences how quickly his shadow moves, the man's distance from the pole is irrelevant.
Pole: Either of two related opposites
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 the man and pole are standing straight up, which means the 2 triangles are similar.
by similarity,
(y−x)/y=5.4/17
17(y−x)=5.4y
17y−17x=5.4y
11.6y=17x
y=85/58x
differentiate both sides with respect to t or time.
dy/dt=85/58 dx/dt
you know dx/dt=5.5 ft/s because the man is walking that speed away from the pole. you want to find dy/dt, how fast the tip of the shadow is moving that means , dy/dt=85/58.5.5 ft/s=8.06 ft/s
since only the man's speed influences how quickly his shadow moves, the man's distance from the pole is irrelevant.
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