related rates, Lamp post

Question

A man 6 feet tall walks at a rate of 8 feet per second away from a light that is 15 feet above the ground



(a) When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?

(b) When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?

Answer 1

dc/dt=-8

db/dt=?

(heigh a)/(height2)=(b starting dist)/(c next point)=

15/6=b/(b-c)

cross mult

(15b-15c)=(6b)

-15c=-9b

5c=3b

3db/dt=5dc/dt

substitute

3db/dt=5*-8

" " =-40

db/dt=-13.333..........mph