Word Problem

Question

A batter hits a baseball in such a way that its path is described by the parabolic function: y = − 0.00126875x2 + 0.5x + 3. A fence of varying height surrounds the baseball ?eld. Given the information in the exercise, determine whether the ball goes over the fence, hits the fence, or hits the ground before reaching the fence. The fence is 380 feet away from the batter, and the fence is 10 feet high.

Answer 1

This problem is essentially asking if the height of the baseball is at least 10 feet at a distance of 380 feet away from the batter.  So, you can plug in 380 for x and solve:

 

f(x) = -0.00126875x² + 0.5x + 3

f(380) = -0.00126875(380)² + 0.5(380) + 3

f(380) = -183.2075 + 190 + 3

f(380) = 9.7925

 

At a distance of 380 feet from the batter, the baseball reaches a height of 9.7925 feet, so the baseball will hit the fence.