Formula of parabola

Question

A softball crosses home plate at a height of 4 feet, and the batter hits the ball. The path of the ball is described by

h=-1/729(x-162)^2+40, where x represents the distance from home plate and h the height of the ball above the ground.

 

a) The outfield wall is 6 feet high and 318 feet from home plate. Will the ball go over the wall for a home run? If so, by how many feet will it clear the wall? 

 

b) Suppose the outfield wall is 326 feet from the home plate. Would it be possible for an outfielder to catch the ball? If so, at what height above the ground would the ball be when she caught it with her back against the wall? 

Answer 1

h(318) = (-1/729)(318-162)² + 40

h(318) = (-1/729)(156)² + 40

h(318) = (-1/729)(24,336) + 40

h(318) = -33.4 + 40

h(318) = 6.6 feet

 

Yes, it will clear the 6 foot wall by 6.6 - 6 = 0.6 feet

 

h(326) = (-1/729)(326-162)2 + 40

h(326) = (-1/729)(164)2 + 40

h(326) = (-1/729)(28,896) + 40

h(326) = -36.9 + 40

h(326) = 3.1 feet

 

At 326 feet from home plate, the ball will be 3.1 feet off the ground.