Answer:
A) 48/13 ft/sec
B) 22/13 ft/sec
Step-by-step explanation: Given that:
A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.
A) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?
Using similar triangles, we can say:
12/L = 55/(L - x)
Cross multiply to get:
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Taking the derivative with respect to time we get:
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
Since dx/dt = 2 so
dl/dt = (12/6.5)(2)
= 24/6.5
= 48/13 ft/sec
B) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole ?
Subtract the rate the shadow is going from the rate the man is going. Therefore
48/13 - 2 = 22/13 ft/sec.
