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Rate of change

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.

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Solution Summary

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).