Part A -

In a major league baseball park, the pitching rubber, where the pitcher stands, is always 60.5 feet from home plate, where the batter stands. In Widget Stadium, the distance from home plate to the wall in center field is 450 feet. A major league baseball pitcher throws a baseball with a horizontal velocity of 132 feet/second. The batter then hits the ball with a horizontal velocity of 141 feet/second, which results in a home run when the baseball passes over the center field fence. The ball passes over the pitching rubber on its way out of the stadium Ignoring gravity and the air resistance that would slow the baseball down, create an equation to model the distance that the baseball is from the pitching rubber once it is thrown. (Hint: distance = velocity time.)

Part B-

Use your equation to determine how long it will take for the baseball to reach home plate. Show your work, and round your answer to the nearest hundredth.

Part C-

Next, again ignoring air resistance and gravity, create an equation to model the distance of the baseball from home plate once it's hit by the batter.

Part D-

Use your equation to determine how long it will take for the baseball to pass over the center field fence. Show your work, and round your answer to the nearest hundredth.

Part E -

Based on the information you've found so far, how many seconds will pass between when the ball is thrown by the pitcher and when the ball passes over the center field fence? Show your work.

Part F -

Next, create an equation to determine the horizontal distance of the baseball from the pitching rubber, starting at the time the ball is hit by the batter. Remember that the ball will pass directly over the pitching rubber, at which time the horizontal distance from the pitching rubber will be zero. So, the ball will get closer at first, then farther away at a constant rate.

Part G -

Using the equations and times you've found so far, create a piecewise equation that models the distance the baseball is from the pitching rubber from the time it's thrown to the time it passes over the center field fence.