The equation of motion of a body of mass m falling under the action of gravity...

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The equation of motion of a body of mass m falling under the action of gravity and subject to an upward aerodynamic drag force f(v) is mv' = mg - f(v) where v(t) is the velocity of the mass as a function of time (v' is the time derivative). First solve the equation for the case where f(v) = cv (c is a constant) with the initial condition v (0) = 0. What is the terminal velocity (V = lim v) of the mass in terms of the model t→∞0 parameters? Next solve the problem with the same initial condition for the case where f(v) = cv². Change the dependent variable from v to u using v = V(t) + 1 U The function V (t) is a particular solution that must be found by trial and error or inspection (e.g., if the nonhomogeneous term is a constant, V(t) is a constant). Solve for V(t) using the original nonlinear equation. How does the terminal velocity compare to the linear drag case? The equation of motion of a body of mass m falling under the action of gravity and subject to an upward aerodynamic drag force f(v) is mv' = mg - f(v) where v(t) is the velocity of the mass as a function of time (v' is the time derivative). First solve the equation for the case where f(v) = cv (c is a constant) with the initial condition v (0) = 0. What is the terminal velocity (V = lim v) of the mass in terms of the model t→∞0 parameters? Next solve the problem with the same initial condition for the case where f(v) = cv². Change the dependent variable from v to u using v = V(t) + 1 U The function V (t) is a particular solution that must be found by trial and error or inspection (e.g., if the nonhomogeneous term is a constant, V(t) is a constant). Solve for V(t) using the original nonlinear equation. How does the terminal velocity compare to the linear drag case?