Two poles are set x = 40 feet apart. Starting at the lowest point, the tightrope walker moves up the rope at a steady rate of 4 ft/sec.

Two poles are set x = 40 feet apart. Starting at the lowest point, the tightrope walker moves up the rope at a steady rate of 4 ft/sec. If the rope is attached y = 20 feet up the pole, express the height h of the walker above the ground as a function of time t. (Hint: Let d denote the total distance traveled along the wire. First express d as a function of t, and then h as a function of d. Assume the tightrope walker begins moving up the rope at t = 0.)