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| PAGE: 181 | SET: Exercises | PROBLEM: 13 |
(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 
.
.gif)
(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.
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