You're almost there! The term dA/dt is the rate of change of length A per unit time, which is precisely the velocity of point A. You were told the velocity of A is 5 ft/s, so there you go:
dB/dt = 2/3 dA/dt = 2/3 (5 ft/s) = 10/3 ft/s.
So here I thought it might be something to formulate a triangle, or actually two:There is a lamp post 15 feet tall casting a shadow 'B' ft. long of a person that is 6 feet tall standing 'A' ft. from the lamp post. If the person moves away from the lamp post at 5 feet per second, how fast does the shadow lengthen?
So the problem is asking me to find the derivative of the shadow's length with respect to time:
I think the triangles are similar:
So we have B and I will attempt to take the derivative of this:
Constant/Chain rules:
Now how do I find the derivative of 'A'? It must have something to do with the movement velocity because it was given information and I haven't used it yet. Unless I am being tricked and it is extraneous/unnecessary information.
You're almost there! The term dA/dt is the rate of change of length A per unit time, which is precisely the velocity of point A. You were told the velocity of A is 5 ft/s, so there you go:
dB/dt = 2/3 dA/dt = 2/3 (5 ft/s) = 10/3 ft/s.