In an Egg Drop competition, one would like to compute the time history of the velocity of the designed egg protection system, which has a mass of .5 kg, an initial velocity of zero, and a drag proportional to the velocity( D = C_d * V, where C_d = .1kg/s). This competition is to take place on earth. The assignment is to solve this problem by:
Solving the equation of motion numerically using three different numerical methods:
(i) Forward difference in time with 1st-order accuracy (i.e. Euler explicit method)
(ii) Backward difference in time with 1st-order accurate (i.e. Euler implicit method)
(iii) Centered difference in time with 2nd-order accuracy.