5.3 Comparison with no-drag model

In a physics or calculus class, you have probably already modeled the vertical motion of a particle by ignoring the drag force. The equation of motion is

m y''[t] = -m g
or y''[t] = -g

and the solution was

In[34]:=

  velocitynodrag[t_] = Integrate[-g, t] + v0

Out[34]=

  -(g t) + v0

In[35]:=

  heightnodrag[t_] = 
                Integrate[Evaluate[velocitynodrag[t]],t] + y0

Out[35]=

       2
  -(g t )
  ------- + t v0 + y0
     2

This model is accurate for objects moving in a vacuum, in which there is no drag force, or sometimes for streamlined objects, such as bullets or rockets, which are designed to have only a small drag force. Both of our models, which include the drag force, are refinements of the no-drag model, but they are also more awkward to use. List some of the extra complications that are involved in using our models. Our models should be compared to the no-drag model for accuracy. On the other hand, it is meaningless to compare the two drag force models with each other. One is designed to model low Reynolds number flows and the other is designed to model high Reynolds number flows. We will compare the drag and no-drag models in some of the applications in Section 6.

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