how fast is the distance from the observer to the balloon increasing when the balloon is 6 feet high?

Question

A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 3 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 6 feet high?

______ feet per second

Answer 1

Distance L = (150² + h²)^0.5; dL/dt = ^hdh/dt/(22500 + h²)^0.5 = 6ft·3ft/s/150.12 ft = 0.12 ft/s