Example 7.  Consider the quadratic drag model for the path of a baseball.  
        
Check out this mathematical model for several cases.

Solution 7.

Remark.  The coefficient  k = 0.002  has been chosen arbitrarily.

Fact.  Willie Stargell was the first player ever to hit a baseball out of Dodger Stadium, with his 506-foot, 6 1/2-inch blast off Alan Foster in 1969 still the longest home run ever hit at the stadium.  
This case gets close to the data point  (506.5, 0).

Fact.  Willie Stargell was the first player ever to hit a baseball out of Dodger Stadium - and he did it twice, the second time with a 470-foot shot off Andy Messersmith in 1973.  
This case gets close to the data point  (470, 0).

Fact.  Mickey Mantle hit a ball May 22,1963:  370 feet from home plate and 115 feet above field level.
This case gets close to the data point  (370, 115).

Fact.  Dick Allen hit a ball July 6,1974:   415 feet and an altitude of 85 feet.
This case gets close to the data point  (415, 85).

(c) John H. Mathews 2004