Week 8 Application
Baseball
Quadratic equations can model the path that objects take when thrown up in the air. Examples can include balls, rockets and fireworks.
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. Be sure to show all supporting work for your solutions.
First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. Add white space around your answers to make them stand out!
- Suppose you are in the stands of a World Series baseball game. A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air.
When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation.
Height = -16t^2 + 96t + 5
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe how the ball travels – what is the shape of its path?
c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.
Note. Your answer, t, will be in terms of seconds.
d. After how many seconds will the ball reach its maximum height?
e. What is the height that the ball will reach?
f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e?
g. How many solutions are there to the equation -16t^2 + 96t + 5 = 0? How do you know?
h. What do the solutions represent? Is there a solution that does not make sense? Why?
