Example 8.  The model in Example 3 is the quadratic drag model.  The following is not.
          
Let's check it out.

Solution 8.

Use the same initial conditions as in the first case in Example 7.

Observe that this is different from our previous result.

    To convince ourselves that the model in Example 3 is correct, recall that velocity is a vector valued function, and its magnitude is  

.  

The tangent vector to the curve is  ,  and the component of air resistance in the direction of the x-axis is  

which simplifies to be  

.  

Similarly, the component of air resistance in the direction of the y-axis is  .  

Hence, the model in Example 7 is correct.  

(c) John H. Mathews 2004