DERIVATIVES

9. A hot air balloon is attached to a spool of rope that is 125 feet away from the balloon when it is on the ground. The hot air balloon rises straight up in such a way that the length of rope increases at a rate of 15 ft/sec. How fast is the hot air balloon rising 20 seconds after it lifts off? Balloon This Length Increasing at 15 ft/sec Spool of Rope 125 ft 10. A rock is dropped straight off a bridge that is 50 meters above the ground and falls at a speed of 10 m/sec. Another person is 7 meters away on the same bridge. At what rate is the distance between the rock and the second person increasing just as the rock hits the ground? Rock Dropped Here 7 meters Person Find Rate This Distance Changing Rock