Answer:
2.5t
Step-by-step explanation:
Let the man be
x
feet away from the street light, and his shadow length be
y
, Let the tip of the shadow be
l
feet away from the light such that
l
=
x
+
y
and we are given that
d
x
d
t
=
2
By similar triangles:
y
6
=
x
+
y
30
∴
30
y
=
6
(
x
+
y
)
∴
30
y
=
6
x
+
6
y
∴
30
y
−
6
y
=
6
x
∴
24
y
=
6
x
∴
y
=
1
4
x
Now,
l
=
x
+
y
⇒
l
=
x
+
1
4
x
∴
l
=
5
4
x
Differentiating wrt
x
gives;
d
l
d
x
=
5
4
And by the chain rule we have:
d
l
d
t
=
d
l
d
x
d
x
d
t
∴
d
l
d
t
=
5
4
×
2
∴
d
l
d
t
=
2.5
feet/sec
