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Answer:
20
3
f
t
s
Explanation:
in this diagram, 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
=
6
15
15
(
y
−
x
)
=
6
y
15
y
−
15
x
=
6
y
9
y
=
15
x
y
=
5
3
x
differentiate both sides with respect to
t
or time.
d
y
d
t
=
5
3
d
x
d
t
you know
d
x
d
t
=
4
f
t
s
because the man is walking that speed away from the pole. you want to find
d
y
d
t
, how fast the tip of the shadow is moving.
that means
d
y
d
t
=
5
3
⋅
4
f
t
s
=
20
3
f
t
s
actually, the man's distance from the pole doesn't matter since only his speed affects how fast his shadow moves