Example 5.  Consider the frictionless model for the path of a baseball.  
          
Check out this mathematical model for several cases.  

Solution 5.

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 Dodger stadium.  
Question.  Would this ball clear the outfield wall of the stadium ?  At x = 400 feet, the height is only about 80 feet high !
The next solution has the same initial velocity, but a slightly larger angle of 47 degrees.

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 Dodger stadium.  
Question.  Would this ball clear the outfield wall of the stadium ?  At x = 400 feet, the height is only about 94 feet high !

Fact.  Willie Stargell was the first player ever to hit a baseball out of Dodger Stadium - and he did it twice, second time with a 470-foot shot off Andy Messersmith in 1973.  
Question.  Would this ball clear the outfield wall of the stadium ?  

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).

Caveat. The above cases with no air resistance seem to fit the position of the final point. However, the initial speeds are  86.6,  86.6,  83.2,  87.3, and  88  miles per hour.  It is believed that a "power hitter" will hit the ball 120-136 mph. Since these initial speeds seem too low, models that include friction are more realistic and will be considered in the next examples.

(c) John H. Mathews 2004