Task 1(2 marks)
Draw a free-body diagrams showing the forces acting on the skydiver during the jump when: (a) in freefall, and (b) with the parachute deployed.
Task 2 (3 marks)
Write expressions for the acceleration components ax and ay. Each of these may be built up as a set of expressions. Write expressions for the two phases of the jump:
(a) During freefall.
(b) With the parachute deployed.
State any assumptions used in the model for acceleration.
Task 3 (5 marks)
Write a Python program that computes the trajectory of the skydiver after leaving the aircraft until landing on the ground. Your program should start with the initial state as discussed above. It should then integrate the equations of motion with small increments of time and save the skydiver’s position, velocity and acceleration at discrete points in time. Terminate the integration process when the skydiver has landed (safely, hopefully).
Task 4 (2 marks)
For CDs = CDp = 0.0, integrate the equations of motion analytically to determine an exact solution for the case of no aerodynamic drag. Demonstrate that your program agrees with your analytic solution. A graphical comparison of the two methods would be one form of demonstration.
Task 5 (3 marks)
Determine a time-step that gives a sufficiently accurate estimate of the trajectory for the case of non-zero aerodynamic drag. Use the time of jump and distance down range in the drop zone as the test criteria. Tabulate the results of your experiment with time-step under headings like:
∆t time of jump (s) distance down range (m) landing speed (m/s)
Explain why you consider the chose time-step to be good enough. What was the landing speed of the skydiver and how long did the jump take?
Task 6 (5 marks)
Produce some plots of the skydiver’s jump.
1. A plot of the trajcetory (x vs y).
2. A plot of the velocity with time. Use time on the x-axis and velocity on the y-axis. Show two curves on this plot: x-velocity and y-velocity.
3. A plot of the acceleration with time. As above but with acceleration on the y-axis and two curves showing x-acceleration and y-acceleration.
Task 7 (4 marks)
As a skydiving operator, you advertise that the jump will last 6 minutes from aircraft exit to landing. On one trip, the maximum mass amongst a group of customers is 80 kg and the minimum mass is 65 kg. You instruct the jumpers to deploy their parachutes at a height of 1400 m. To what altitude does the aircraft need to climb at the beginning of the jump so that the customers get a 6-minute jump time? Use your pro
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