Related Rates: Two Shadows (Larson p.162 #9)
Explore the sketch. Work towards understanding how changing something makes other things change.
Let CA represent the man and FE represent the boy.
1) Use the sketch to answer the following:
a) When does the man's shadow extend past the boy's shadow?
b) When is it the reverse situation-- the boy's shadow extends past the man's shadow?
c) When do the tips of the two shadows coincide?
2) Find analytically the distance the man is from the pole when the tips of the two shadows coincide.
3) Press the animate button. What is happening with how fast the length of the shadows are changing? Do they change at the same rate? Why?
4) Determine analytically the rate of change of the tip of the man's shadow as a function of the his distance from the light pole if he is walking towards the light pole at a rate of 5 meters per second.