This activity is intended to supplement Calculus, Chapter 3, Lesson 4.
Part 1 – Bungee Jump
In June 2001, the record for the longest bungee jump was shattered when a stuntman jumped from a helicopter hovering over 10,000 feet. This “Mile Long Bungee Jump” is illustrated using the following parametric equations:
2. What physical quantity is given by the second derivative of position?
3. Within the first 40 seconds, when do (does) the extrema for the velocity occur? Show your work.
4. The third derivative of position with respect to time is known as jerk. After the first time the velocity is zero, when does jerk have the largest magnitude?
5. When is the downward velocity at a maximum? What is the speed at that time?
6. Write at least two complete sentences relating position-time, velocity-time, and acceleration-time graphs from the helicopter bungee jump situation.
On the acceleration-time graph, the mathematical model is not realistic for the first 4 seconds, but it is after that. Change the window settings so that you can no longer see the first 4 seconds of the acceleration-time graph.
8. What is the point of inflection where the graph changes from concave up to concave down in the first 40 seconds? Use the Inflection Point tool (F5:Math > 8:Inflection).
Part 2 – Graphically examine another situation