# calculus

Consider the motion of a particle of mass m falling vertically under the earth’s gravitational field, and suppose the
downward motion is opposed by a frictional force p(v) dependent on the velocity v(t) of the particle. Then the
velocity satisfies the equation
mv0(t) = 􀀀mg+ p(v); t � 0
Let m = 1kg, g = 9:8m=sec2, and v(0) = 0. Using Euler’s, Heuns’, and Classical Runge-Kutta methods, solve the
differential equation for 0 � t � 20 and for the following choices of p(v):
1. p(v) = 􀀀0:1v
2. p(v) = 0:1v2
Find the answers to at least four digits accuracy. Graph the function v(t). Compare the solutions.

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