Foul Ball from the Third Deck: - High School Math Help



Quadratic equations: Projectile motion

Part 1: Hitting a Homerun:

Ryan Doumit hits a homerun at PNC Park. Use this equation to

model the flight of the ball.

h(t) = [pic]

In this equation, y is the number of feet above the ground, t is the time in

seconds from the moment the ball was hit, v is the initial vertical velocity (or

speed) in feet per second, and [pic] is the initial height the ball is hit from.

Suppose Ryan’s bat hits the ball at a level that is 4 feet above the field, and

the initial vertical velocity of the ball is 96 feet per second.

1. Write the equation for Ryan Doumit’s homerun.

2. What is the independent variable?

What is the dependent variable?

3. Complete the table. Be sure to include labels.

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4. From the table when will the ball hit the ground?

5. From the table when will the ball be at its highest point?

6. On a separate piece of graph paper make a graph for your data.

7. Does the graph support your answers for questions 4 and 5, why or why not?

8. Using your graph and table, when will the ball have a height of 84 ft? 148ft? 150 ft?

9. Using your graph and table, when is the ball 10 ft off the ground?

Quadratic Formula: [pic]

The quadratic formula is method for solving for the zeros of quadratic equations, given a quadratic function in standard form. ([pic])

10. Rewrite the model you found in question 1 and set it equal to 0

11. Remember the standard form of a quadratic function is [pic]

From the model identify a_________ b___________ c_____________

12. Plug a, b, and c into the quadratic formula and simplify. (The [pic]indicates two different problems, one with a + sign, and one with a – sign)

13. Exactly how long did it take the ball to hit the ground?

14. If we want to determine when the ball was 10ft off the ground, what would we need to change in the equation? Write the new equation.

15 The quadratic formula is only used to solve for zeros of a function. What do you need to do first in order to use the quadratic formula?

16. Use the quadratic formula to solve for when the ball is 10 feet off the ground.

17. Does it make sense that you got two different answers? Why?

Part 2: Punting:

Daniel Sepulveda is attempting to punt the ball down field. The height of the football (feet) at any given time, t (sec) is modeled by: h(t) = [pic]

1. What is the initial velocity at which he kicks the ball?

2. What is the independent variable? What is the dependent variable?

3. Complete the table. Be sure to include labels.

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4. From the table when will the ball hit the ground?

5. Use the quadratic formula to determine exactly when it hits the ground?

6. From the table when will the ball be at its highest point?

7. On a separate piece of graph paper make a graph for your data.

8. Does the graph support your answers for questions 11 and 13, why or why not?

Finding the Vertex of a quadratic function.

Given a quadratic function f(x) = [pic], the x-value of the vertex can be found using [pic],

9. For your function identify a__________ b____________ c______________

10. Find the x-value of the vertex using the formula above.

11. How can we find the y-value of the vertex?

12. What is the vertex of this function? What does it mean for this situation?

13. State the domain ______________ Range _______________

Practice Problem.

Kicking the ball

A ball is kicked down the football field. It’s height with respect to its distance downfield can be modeled by h(x) = [pic] measured in yards

1. Determine the maximum height of the ball? How far down field is it at its maximum height?

2. How far downfield will the ball hit the ground?

3. If this kicker was attempting a 30 yard field goal and the cross bar of the field goal post is 10 ft off the ground. Would the attempt be good?

4. What is the longest field goal this kicker could make?

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