Calculus Rates of Change

Question

Nemo is standing at point A which is 20 feet away from a balloon when the balloon starts to rise at 5 ft/sec. At the instant the balloon is 21 feet high, how fast is the straight-line distance between Nemo and the balloon changing?

Answer 1

The straight-line distance of Nemo to the balloon is d = (20+y)^1/2 With related rate problems you usually take the derivative of the two variables with respect to t:

dd/dt = (20+y)^-1/2 dy/dt You know all the terms on the RHS. The LSH is what is asked for.