Math 326, Feb 3 - If
Tom Can Do It, So Can We - Part 2
We continue our model of Ethan jumping from a skyscraper. In part 1, we
estimated how fast Ethan was falling when the cable became taut. Now we model
the swing. There are a lot of vectors involved.
First, not all of the falling velocity is converted into swinging velocity.
Some is absorbed by the cable (as well as by Ethan's bruised and battered body).
Also, the acceleration due to gravity is partly absorbed by the cable. We
calculate and update both depending on the angle of the cable at that particular
time.
Additional Questions
- Include air resistance in the model. Air resistance gives
an acceleration of c|v|2 in the opposite direction as
velocity, in this case the opposite of the direction of the swing.
Use for the constant c=0.001358 as before.
- Build an animated graph which follows Ethan's swing.