1. First do some research and identify a real example where you can determine both the mass and the tenninal velocity of some real falling object. The object could be a skydiver or a parachutist, or it could be an object falling through a uid. Make note of the value of the mass, m , of the object and the terminal velocity, \"T of paragraphs describing your example. Be sure to cite your source(s}. dv = g Irv.\" m 2. For the force model R : kV , the acceleration is if! . In this , for your example. Write a couple equation, of , (E , and k are constants. This equation is a separable differential equation, something covered near the end of the second unit. Your rst task will be to use your computer algebra system to determine the general solution to this differential equation. You will next use your computer algebra system to produce the particular solution for an object that is dropped far above ground, with Um) = . Use the mass and terminal velocity from your research to compute the value of k . Use a computer algebra system to graph and conrm the terminal velocity by Iexamining the limit of the particular solution. You may also want to solve this differential equation by hand for comparison. Be sure to copy the graph for your example into your report. Write a couple of paragraphs describing the results for your example in your report. oh: 2 = g Kid r' m 3. For the force model R : KP , the acceleration is RIF Your next task will be to use your computer algebra system to determine the general solution to the second separable differential equation. The main changes from the conunands used for your rst model will be related to the differences between the two models, R = 121' and R = K\": , the d d lzgkpfm lzgKvlfm differential equations, tiff and ll , and the m m \"if =_ vi = f: tenninal velocities, k and f1 . You should keep the same mass and tenninal velocity from your research, which you used in with the rst model. Use your computer algebra system to detennine the general solution to this differential equation. You then next use your computer algebra system to produce the particular solution for an object that is dropped above ground, where V(0) =0 . Use the mass and terminal velocity from your research to compute the value of A (for the model R = Kv" ). Use a computer algebra system to graph and confirm the terminal velocity by examining the limit of the particular solution. You may want to solve this differential equation by hand for comparison. Be sure to copy the graph for your example into your report. Write a couple of paragraphs describing the results for your example in your report. 4. Write a one or two paragraph summary of what you learned from this project