Assuming that drag is proportional to the square of velocity

Question: Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following differential equation:

where u is velocity (m/s), t = time (s), g is the acceleration due to gravity (9.81 m/s^2), cd = a second-order drag coefficient (kg/m), and ,n = mass (kg). Solve for the velocity and distance fallen by a 90-kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine when it hits the ground. Obtain your solution with (a) Euler’s method and (b) the fourth-order RK method.

Solution:

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