If air resistance is proportional to the square of the
Chapter 9, Problem 13E(choose chapter or problem)
If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from
\(m \frac{d v}{d t}=m g-k v^{2}\), k > 0.
Let v(0) = 0, k = 0.125, m = 5 slugs, and \(g=32 \mathrm{ft} / \mathrm{s}^{2}\).
(a) Use the RK4 method with h 1 to approximate the velocity v(5).
(b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6].
(c) Use separation of variables to solve the IVP and then find the actual value v(5).
Text Transcription:
g=32 mathrm ft / mathrm s^2
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