11.03 Quadratics Application Name ____________________

Fireworks Assessment Date ____________ Per. ____

At a fireworks display celebration, a fireworks rocket is launched upward from the ground with an initial velocity of 160

feet per second. Spectators watch and wonder how high the rocket will go before it begins to descend back to the

ground.

The formula for vertical motion is h(t) = -16t2 + vt + s, where v is the initial velocity (v) and (s) is the initial height. Time t

is measured in seconds, and height h is measured in feet.

1. What function describes the height, h in feet, of the rocket t seconds into the launch?

_________________________

2. Graph the position of the rocket as a function of time.

3. What is a reasonable domain and range for this situation?

Domain _________________________ Range _________________________

4. How high is the rocket after 3 seconds into the launch? When does it reach this height again?

____________ ____________

5. For the safety of the audience, the rocket, as it descends, should be set to explode at least 250 feet off the ground.

The operator has a choice of fuses to use to explode the rocket. Fuse A will detonate the rocket between 3 and 5

seconds, Fuse B will detonate it between 4 and 6 seconds, and Fuse C will detonate it between 6 and 8 seconds.

Which fuse should be used? Why?

6. Suppose the rocket is launched from the top of a 200-foot tall building. How will this change the position function

for the rocket?

7. How will the graph of the new position function compare with the graph of the first position function? What does

the new graph tell you about the situation?

time height

Algebra Assessments © 2002 The Dana Center

Analyze the following situations below and answer the questions.

Batter Brandon hit a baseball upward with an initial speed of 120 feet per second. How much later did Ollie Outfielder

catch the ball? (Use the formula, h(t) = -16t2 + vt + s)

1. If v = initial velocity (initial speed), what is the initial velocity? _________________

2. What is the function? _________________

3. What was the maximum height of the ball? _________________

4. How long did it take to reach maximum height? _________________

5. How much later did Ollie catch the ball? _________________

6. What is a reasonable domain for this situation? _________________

Bart tossed an apple to Starr, who was on a balcony 40 feet above him, with an initial velocity of 56 feet per second.

Starr missed the apple on the way up, but caught it on the way down. How long was it in the air?

(Use the formula, h(t) = -16t2 + vt + s )

7. If v = initial velocity (initial speed), what is the initial velocity? _________________

8. What is the function? _________________

9. What was the maximum height of the apple? _________________

10. How long did it take to reach maximum height? _________________

11. How long was the apple in the air? _________________

12. What is a reasonable range for this situation? _________________

A signal flare is fired upward with an initial speed of 245 meters per second. A stationary balloonist at a height of 1960

meters sees the flare on its way up. How long after this will the flare pass the balloonist again on the way down?

(Use, h(t) = -4.9t2 + vt + s )

13. What is the initial velocity? _________________

14. What is the starting height? _________________

15. What is the function? _________________

16. How long was the flare at least 2940 meters above the ground? _________________

17. What is the maximum height of the flare? _________________

18. How long was the flare in the air? _________________