Flight of the Golf Ball
Algebra 2 Exploring Quadratic Graphs Name ______
For 7.2 12
Flight of the Golf Ball
An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, can be determined by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
The vertical height of a golf ball hit from ground-level as a function of time is given by the equation represents
h(t) = –16t² + 96t.
1. Create a table of values for time from 0 to 6 seconds in increments of 0.5 seconds. Use this table to graph the height of the golf ball at a given moment in time.
Time [seconds] / 0 / 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 / 3.5 / 4.0 / 4.5 / 5.0 / 5.5 / 6.0Height [feet]
2. What is the maximum height reached by the golf ball and when does this happen? Explain how you know.
3. a. When does the ball hit the ground?
Explain how you know.
b. At what other time was the ball on the ground?
c. How does the time when the ball reached its maximum height relate to the times when the ball was on the ground?
4. a. When is the ball at a height of 100 feet? Explain how you know.
b. When is the ball at a height of 40 feet? Explain how you know.
c. How does the time when the ball is at the maximum height relate to when the ball is at a height of 100 feet? … 40 feet?
Flight of the Golf Ball
5. The flight of another golf ball can be modeled by the following equation: h(t) = –16(t – 3)² + 144
a. Use the table below to find values for time from 0 to 6 seconds in increments of 0.5 seconds.
Time [seconds] / 0 / 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 / 3.5 / 4.0 / 4.5 / 5.0 / 5.5 / 6.0Height [feet]
b. Use this table to graph the height of the golf ball at a given moment in time. Graph on the same graph as question #1.
6. What was the maximum height the golf ball reached on the second graph and when did it happen?
7. At what times was the ball on the ground?
8. Which question [question #6 or #7] did this form of equation provide direct information about? What information did the equation provide?
9. If you were given the following equation to describe the path of a golf ball, what information would you know without having to actually graph the equation: f(t) = –16(t – 8)2 + 70 ?
10. The flight of another golf ball can be modeled by the following equation: h(t) = (–16t)(t – 6).
a. Use the table below to find values for time from 0 to 6 seconds in increments of 0.5 seconds.
Time [seconds] / 0 / 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 / 3.5 / 4.0 / 4.5 / 5.0 / 5.5 / 6.0Height [feet]
b. Use the table to graph the height of the golf ball at a given moment in time. Graph on the same graph as questions #1 and #5.
c. What is the maximum height of the ball? ______
d. When was the ball on the ground? ______
11. What information does this third form of quadratic equation provide?
12. If you were given the following equation to describe the path of a golf ball, what would you know without having to actually graph the equation: –16t(t – 10)?
13. If you were given the following equation to describe the path of a projectile [the path is called a parabola], what would you know without having to actually graph the equation: f(t) = (t + 5)(t – 10)?
The height of a projectile can be modeled by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
a. If you were given the following equation to describe the path of a projectile, what would you know without having to actually graph the equation h(t) = –16t² + 100t + 20.
b. What does the 20 represent in this equation? Explain what it means.
c. What does the term –16t² represent in this equation? [what would happen to the height of the projectile without it?]
Blast Out of Space
An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, can be determined by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
The vertical height of a toy rocket as it blast off from ground-level as a function of time is given by the equation
h(t) = –16t² + 80t.
1. Create a table of values for time from 0 to 5 seconds in increments of 0.5 seconds. Use this table to graph the height of the rocket at a given moment in time.
Time [seconds] / 0 / 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 / 3.5 / 4.0 / 4.5 / 5.0Height [feet]
2. What is the maximum height reached by the toy rocket and when does this happen? Explain how you know.
3. a. When does the rocket hit the ground?
Explain how you know.
b. At what other time was the rocket on the ground?
c. How does the time when the rocket reached its maximum height relate to the times when the rocket was on the ground?
4. a. When is the rocket at a height of 100 feet? Explain how you know.
b. When is the rocket at a height of 25 feet? Explain how you know.
c. How are the times you found related to each other and to the maximum height?
Football Frenzy
An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, can be determined by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
The vertical height of a football as it is kicked from ground-level as a function of time is given by the equation
h(t) =–16t² + 72t.
1. Create a table of values for time from 0 to 4.5 seconds in increments of 0.25 seconds. Use this table to graph the height of the football at a given moment in time.
Time / 0 / 0.25 / 0.5 / 0.75 / 1.0 / 1.25 / 1.5 / 1..75 / 2.0 / 2.25 / 2.5 / 2.75 / 3.0 / 3.25 / 3.5 / 3.75 / 4.0 / 4.25 / 4.5Height
2. What is the maximum height reached by the football and when does this happen? Explain how you know.
3. a. When does the football hit the ground?
Explain how you know.
b. At what other time was the football on the ground?
c. How does the time when the football reached its maximum height relate to when the football was on the ground?
4. a. When is the football at a height of 100 feet? Explain how you know.
b. When is the football at a height of 20 feet? Explain how you know.
c. How are the times you found related to each other and to the maximum height?
World Cup Soccer
An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, can be determined by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
The vertical height of a soccer ball as it is kicked from ground-level as a function of time is given by the equation
h(t) = –16t² + 48t.
1. Create a table of values for time from 0 to 3 seconds in increments of 0.25 seconds. Use this table to graph the height of the soccer ball at a given moment in time.
Time / 0 / 0.25 / 0.5 / 0.75 / 1.0 / 1.25 / 1.5 / 1..75 / 2.0 / 2.25 / 2.5 / 2.75 / 3.0Height
2. What is the maximum height reached by the soccer ball and when does this happen? Explain how you know.
3. a. When does the soccer ball hit the ground?
Explain how you know.
b. When else was the soccer ball on the ground?
c. How do these two times relate to the time it took for the soccer ball to reach its maximum height?
4. a. When is the soccer ball at a height of 100 feet? Explain how you know.
b. When is the soccer ball at a height of 15 feet? Explain how you know.
c. How are the times you found related to each other and to the maximum height?
I’d Rather Throw a Ball in the Air by Myself than Do Math
An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, can be determined by the following equation: h(t) = at2 +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.
The vertical height of a ball as it is thrown from ground-level as a function of time is given by the equation
h(t) = –16t² + 25.6t.
1. Create a table of values for time from 0 to 1.6 seconds in increments of 0.1 seconds. Use this table to graph the height of the ball at a given moment in time.
Time / 0 / 0.1 / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8 / 0.9 / 1.0 / 1.1 / 1.2 / 1.3 / 1.4 / 1.5 / 1.6Height
2. What is the maximum height reached by the ball and when does this happen? Explain how you know.
3. a. When does the ball hit the ground?
Explain how you know.
b. When else was the ball on the ground?
c. How do these two times relate to the time it took for the ball to reach its maximum height?
4. a. When is the ball at a height of 6 feet? Explain how you know.
b. When is the ball at a height of 100 feet? Explain how you know.
c. How are the times you found related to each other and to the maximum height?
