1. A weather balloon is rising vertically at a constant rate of 4 ft/s directly above a straight and level road. When the balloon is 75 ft above the road, a car moving at 55 ft/s passes directly under the balloon. Based on this information find:
a. the rate the distance between the balloon and the car is changing 3 sec after the car has passed under the balloon
b. the rate of change of the area of the triangle 1 min after the car has passed under the balloon. Note: The balloon continues to rise after the car passes underneath.
2. During a sailboat race, a boat is 2 miles west of and sailing at 6 mph toward a maker buoy. At the same time, a 2nd boat, that is ahead of the 1st boat, is 3 miles north of the marker buoy and sailing away form the buoy at 9 mph. Based on this situation, find each of the following:
a. the rate the (straight) distance between the boats is changing
b. the rate theta is changing 10 min from the given initial conditions.
This shows how to find the rate of change in two situations: a weather balloon (distance between balloon and car and area of triangle between balloon and car) and a sailboat race (distance between boats and angle between boats).