This question isn't really on related rates. I just wanted to ask whether or not if a man is walking away from a lamp post, that would increase the length of his shadow. Or if that is just the question, and not true. And if it is true, that if a person walks away from a lamp post, increases the length of his/her shadow, can you please explain.
Yes it is true. To see it, just draw two diagrams, one close and one far from the lamppost.
In each case, draw a horizontal line to represent the ground. Represent the lamppost by a vertical line, and the man by a shorter vertical line, each sitting on the ground.
Draw a line from the top of the lamppost to the top of the man, and continue it until it hits the ground. This represents a ray of light which just clears the man's head and hits the ground.
Thicken the part of the ground between the man and the point where the ray of light hits the ground. This is the shadow. This is because if you pick any point on the ground in the shadow, you cannot draw a straight line to the lamppost without going through the man.
Alternatively, why not go out into the street tonight and prove it to yourself.
