A woman 5 ft tall walks at the rate of 7.5 ft/sec away from a streetlight that is 10 ft above the ground. At what rate is the tip of her shadow moving?

Height of the woman = 5 ft

Rate at which the woman is walking = 7.5 ft/sec

Let us assume the length of the shadow = s

Le us assume the distance of the woman's feet from the base of the streetlight = x

Then

s/5 = (s + x) / 12

12s = 5s + 5x

7s = 5x

s = (5/7) x

Now let us differentiate with respect to t

ds/dt = (5/7) (dx/dt)

We already know that dx/dt = 7/2 ft/sec

Then

ds/dt = (5/7) * (7/2)

= (5/2)

= 2.5 ft/sec

From the above deduction, it can be easily concluded that the rate at which the tip of her shadow is moving is 2.5 ft/sec.