OVERVIEW:

In the previous parachute task, a skydiver starts at 4000 m and descends for 60 seconds at which time his chute opens instantaneously. In this task, however, we will incorporate chute deployment which occurs over a few seconds. During chute deployment, the effects of the drastic changes in chute area can be approximated using the polynomial equation shown below. Copy your script from task 2 to begin task 3 and follow the direction s below. (Note: in step 3, you are asked to record the acceleration values experienced during the jump.)

STEP 1: CHANGE SIMULATION TO REFLECT PARACHUTE OPENING

In the original simulation, the k/m value changed immediately. This immediacy is unrealistic; and for a skydiver, the acceleration resulting from such an immediate change would cause serious injury. Therefore, between the free-fall stage (first 60s) and the fully opened canopy stage, insert another stage where the parachute deploys for a nonzero (3.2 seconds) length of time.

STEP 2: PARACHUTE OPENS IN 3.2 SECONDS

The chord to open the parachute is pulled after 60 seconds of free fall. The skydiver starts to slow down as the simulation drag coefficient (k/m) changes from 1/6 to 5/3 but the chute does not open immediately On average, it takes 3.2 seconds for the parachute to fully deploy. However, the rate of change from 1/6 to 5/3 is not a linear relationship; indeed, k/m is better represented by a polynomial:

k/m= -0.0865*td^3+ 0.429*td^2+ 1/6

where td is the time after deployment in seconds (ranges from 0 to 3.2s)

Example 1: Time = 60s, then td = 0s and the equation results in k/m = 1/6 (td terms cancel out).

Example 2: Time = 61s, then td = 1s and the equation results in k/m = .5092

STEP 3: CALCULATE ACCELERATION AS EXPERIENCED BY THE SKYDIVER

By definition a=dv/dt, so the acceleration of the skydiver as a function of time is:

a = g–(k/m)*v.

Calculate and record acceleration at every time (ex. a(i + 1) = g-(k/m)* v).

STEP 4: REFORMULATE VELOCITY CALCULATION

With the calculation of a in step 3, remove any instances of ?v for a.

Example: v(i + 1) = v(i) +?v*dt --> v(i + 1) = v(i) + a*dt

STEP 5: PLOT RESULTS OF SIMULATION

Make plots of height, velocity and acceleration versus time using subplot after the simulation is complete.