Answer:
The rate of change of the shadow length of a person is 2.692 ft/s
Solution:
As per the question:
Height of a person, H = 20 ft
Height of a person, h = 7 ft
Rate = 5 ft/s
Now,
From Fig.1:
b = person's distance from the lamp post
a = shadow length
Also, from the similarity of the triangles, we can write:
[tex]\frac{a + b}{20} = \frac{a}{7}[/tex]
[tex]a = \frac{7}{13}b[/tex]
Differentiating the above eqn w.r.t t:
[tex]\frac{da}{dt} = \frac{7}{13}.\frac{db}{dt}[/tex]
Now, we know that:
Rate = [tex]\frac{db}{dt} = 5\ ft/s[/tex]
Thus
[tex]\frac{da}{dt} = \frac{7}{13}.\times 5 = 2.692\ ft/s[/tex]
