Posted by Jake on .
A hot-air balloon is 180 ft above the ground when a motorcycle passes directly beneath it (travelling in a straight line on a horizontal road) going at a constant speed of 60 ft/s. If the balloon is rising vertically at a rate of 15 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 20 seconds after the motorcycle was directly beneath the balloon.
draw the figure, a right triangle. figure out distances after 20seconds.
let horizontal distance be x, height be h, and d the slant distance.
2d dd/dt= 2h dh/dt+2x dx/dt
solve for dd/dt, you know all else.