Answer:
Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.
Step-by-step explanation:
Given : In the figure attached, Length of girl EC = 4 ft
Length of street light AB = 25 ft
Girl is moving away from the light with a speed = 6 ft per sec.
To Find : Rate () of the tip (D) of the girl's shadow (BD) moving away from th
light.
Solution : Let the distance of the girl from the street light is = x feet
Length of the shadow CD is = y feet
Therefore, feet per sec. [Given]
In the figure attached, ΔAFE and ΔADE are similar.
By the property of similar triangles,
25x = 21(x + y)
25x = 21x + 21y
25x - 21x = 21y
4x = 21y
y =
Now we take the derivative on both the sides,
=
=
≈ 1.14 ft per sec.
Since w = x + y
Therefore,
= 7.14 ft per sec.
Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.
