1. The document investigates the type of hit required to hit a home run based on the distance from home plate to the left field wall at Fenway Park. 2. It analyzes 12 different trajectories modeled by equations to determine if the ball would reach the necessary height and distance to clear the wall. 3. Key factors that determine if a home run is possible are whether the graph of the equation heads up or down, and the maximum height reached by the ball as modeled in the equation.

1. Hitting a Home Run
Introduction
The left field wall in Boston’s Fenway Parkis100m from home base and the
wall is 10 high.
The purpose of this investigation is to determine the type of hit required to get
a home run.
Mathematical Calculations
Part1
1. Hamish hits the ball according to the following trajectory: y= 5x
Theballhitstheground when y=0
Solve the equation to find whether the ball will land
2. Graph this equation
3. What does the graph look like? Is this kind of hit possible? CanHamish get a home run?
Part2
1. Xander hits the ball according to the following trajectoryy= (x+7)(x+3) +2(x+7)
2. Factorise this equation here:
3. Find the solutions for (x+7)(x+3) +2(x+7)=0
4. Graph this solution
5. What does the graph look like? Is this kind of hit possible? CanXander get a home run?
Part3
1. Mae hits the ball according to the equation 3(x-2)-7(x-2)
2. Factorise this equation here:
3. Find the solutions for 3(x-2)-7(x-2)=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit realistic? Can Maeget a home run?
Part4
1. Mia hits the ball according to theequation y=5x2-20
2. Factorise this equation here:
3. Find the solutions for 5x2-20=0
Source: https://en.wikipedia.org/wiki/Baseball

2. 4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? Will Mia hit a home run?
Part5
1. Prachi hits the ball according to the equation y=x2-10000
2. Factorise this equation here:
3. Find the solutions for x2-10000=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? Will
Prachi hit a home run?
Part6
1. Amber hits the ball according to the equation y=-x2+10000
2. Factorise this equation here (by first removing -1 as a common factor):
3. Find the solutions for -x2+10000=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible?
6. Will Amber hit a home run?
7. Did she hit from home base?
Part7
1. Emily hits the ball according to the equation x2 +12x +36
2. Factorise this equation here:
3. Find the solutions for x2 +12x +36=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? Will Emily hit a home run?
Source:http://www.real-world-physics-problems.com/physics-of-hitting-a-
baseball.html

3. Part8
1. Tim hits the ball according to the equation y= -x2 -12x -36
2. Factorise this equation here (by removing -1 as a factor)
3. Find the solutions for -x2 -12x -36=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? Will Emily hit a home run?
Part9
1. Clairehits the ball according to the equation -x2 +7x -10
2. Factorise this equation here (by removing -1 as a factor)
3. Find the solutions for -x2 +7x -10 =0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? Will Clairehit a home run?
Part10
1. Josh hits the ball according to the equation -x2 +99x+100
2. Factorise this equation here (by removing -1 as a factor)
3. Find the solutions for -x2 +99x+100 =0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? How high did the ball go?
6. Will Josh hit a home run?
7. Did he start from home plate?
8. Would the ball make it over the wall?

4. Part11
1. Willis hits the ball according to the equation y= -x2 +108x+220
2. Factorise this equation here (by removing -1 as a factor)
3. Find the solutions for -x2 +108x+220=0
4. Graph this equation
5. What does the graph look like? Is this kind of hit possible? How high did the ball go?
6. Will Willis hit a home run?
7. Did he start from home plate?
8. Would the ball make it over the wall?
Part12
1. Adam hits the ball according to the equation y=-0.01(x2-99x-100)
1. Factorise this equation here (by leaving -0.01 at the front)
2. Find the solutions for y=-0.01(x2-99x-100)
3. Graph this equation
4. What does the graph look like? Is this kind of hit possible? How high did the ball go?
5. Will Adam hit a home run?
6. Did he start from home plate?
7. Would the ball make it over the wall?
Discussion
1. Can you work out what part of the equation changes the graph
from: heading up to heading down?
2. Can you work out what part of the equation changes the height of
the ball?
Source: https://www.stubhub.com/baseball-tickets/category/29/