Related Rates – Increasing Angle of Elevation (Watching a Hot Air Balloon) скачать в хорошем качестве

Related Rates – Increasing Angle of Elevation (Watching a Hot Air Balloon)

This example of an observer watching a hot-air balloon rise is a standard related-rates exercise for Calculus. We are asked to compute the rate of change of an increasing angle of elevation as the balloon rises. That is, we are computing the change in angle (theta) with respect to time. The solution involves forming a right triangle with theta at the observer. Here are the steps we follow, which are standard for related rates: 1. Read and re-read the problem to gain an intuitive understanding. Sketch a diagram, if possible. Identify rates that are given and the rate that is to be determined. 2. Write an equation that relates the various quantities of the exercise. If necessary, use geometry to eliminate a variable. 3. Use the Chain Rule to differentiate both sides with respect to t. 4. Substitute known values and solve for the desired quantity. 5. Check that the answer is reasonable. ADA-compliant subtitles/captions.