A hot air balloon is 190 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 45 mi/hr (66 ft/s). If the balloon rises vertically at a rate of 7 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 8 seconds later? Let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon. Write an equation relating x, y, and z.
z² = x² + y²
Differentiate both sides of the equation with respect to t.
(___) dx/dt + (___) dy/dt = (___) dz/dt
The rate of change of the distance between the motorcycle and the balloon after 8 seconds is about (Round to two decimal places as needed.)