A differential equation for the velocity v of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity is m (d v)/(d t)=m g-k v^2, where k > 0 is a constant of proportionality. The positive direction is downward.(a) Solve the equation subject to the initial condition v(0)=v0 (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. We saw how to determine the terminal velocity without solving the DE in Problem 41 i
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SOLVED:Suppose that the position of a falling object is governed by the following differential equation, (d^2 x)/(d t^2) (c)/(m) (d x)/(d t)-g=0 where c= a first-order drag coefficient =12.5 kg / s, m= mass = 70 kg, and g= gravitational acceleration =9.81 m / s^2 . Use the shooting method to solve this equation for position and velocity given the boundary conditions, x(0)=0 and x(12)=500.
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