hi guys can you please help me with this problem:
A street light is mounted at the top of a 15ft-tall pole. A man 6ft tall walks away from the pole with a speed of 5ft/s along a straight path. How fast is the tip of his shadow moving when he is 40ft from the pole?
is this picture I made the right idea?
I don't quite see the relevance of the 6ft since the line reaches from the top anyway. I believe I use tan =opposite/adjacent
First why are you trying to use the tangent function? Second you are making the classic error in related rate problems you are substituting known values too soon (before you have taken the time derivative.)
x is the distance from the pole to the man and y is the distance from the man to the tip of his shadow.
So you need to ask yourself what quantities do we need and how are the related?
The only known information is that
See if you can finish from here.