The Tower Jump

All midshipmen must (see P.E. requirements) jump from a 10 meter diving tower. This applet simulates their position versus time function during such a jump. It uses 10 m/s² to approximate the acceleration due to gravity (a more accurate figure would be 9.8 m/s²).

With the two radio buttons at the bottom of the applet, choose to plot either tangent lines (with a single mouse click on the curve) or secant lines (with two mouse clicks on the curve). Only the cursor's time coordinate needs to be accurate. At most 10 of each line type can be drawn without restarting. These lines, together with the grid lines, can help in analyzing the jumper's average and instaneous velocities at various parts of the jump.

Draw various tangent lines and secant lines. Can you see where the steepest and least steep slopes occur? When the two secant points are close together, will the line they determine be close to tangent lines at nearby points? When you think you have a good feel for these concepts, try filling in the "lab report" for the Tower.

The code for the applet above is online.

To USNA homepage

To Math homepage

To Calc Labs homepage

USNA Mathematics Department
Comments to: Professor Carol G. Crawford, at cgc@nadn.navy.mil or Professor Mark D. Meyerson, at mdm@nadn.navy.mil