A parachutist of mass m is falling in the Earth's gravitational field. We model the situation...

  

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A parachutist of mass m is falling in the Earth's gravitational field. We model the situation as a point mass under the influence of the gravitational force mg and a retarding force assumed proportional to the first power of the instantaneous velocity. Solve the Linear DE with an integrating factor. Newton's 2nd Law provides the DE and we take the initial condition as v(0)=0.. Thus have the IVP dv m dt =mg-kv, v(0) = 0. m, k and g are positive constants. a. Write the Integrating Factor b. Write general soln in terms of a constant, C. c. Evaluate the constant of integration. d. Write the particular solution Find the terminal velocity, i.e. Lim v(t). (-90 v(t) = C= v(1) Lim v()= 1-0 A parachutist of mass m is falling in the Earth's gravitational field. We model the situation as a point mass under the influence of the gravitational force mg and a retarding force assumed proportional to the first power of the instantaneous velocity. Solve the Linear DE with an integrating factor. Newton's 2nd Law provides the DE and we take the initial condition as v(0)=0.. Thus have the IVP dv m dt =mg-kv, v(0) = 0. m, k and g are positive constants. a. Write the Integrating Factor b. Write general soln in terms of a constant, C. c. Evaluate the constant of integration. d. Write the particular solution Find the terminal velocity, i.e. Lim v(t). (-90 v(t) = C= v(1) Lim v()= 1-0