(a)

Height of the pole is ft.

Height of the man is ft.

Speed of the man walking away from the pole is ft/sec.

(b)

Speed of the tip of the shadow .

(c)

Diagram of the situation at any time .

(d)

From the above figure, 

Surface area of the sphere is .

Height of the pole ft.

Height of the man  ft.

Consider length of the shadow ft.

Consider distance between the man and the pole is ft.

From the figure .

Since the triangles and are similar, then

.

Substitute corresponding values in above expression.

Distance between the pole and tip of the shadow is .

Substitute in .

Distance between the pole and tip of the shadow is .

(e)

Speed of the tip of the shadow is .

Consider .

Differentiate on each side with respect to .

.

Speed of the man ft/sec.

Speed of the tip of the shadow is ft/sec.

(a)

A street light is mounted at the top of a  ft tall pole.

Height of the man is ft.

Speed of the man is ft/sec.

(b) Speed of the tip of the shadow.

(c)

(d) Distance between the pole and tip of the shadow is .

(e) Speed of the tip of the shadow is ft/sec.