1. 9-4 Quadratic Equations and Projectiles
A model rocket is shot at an angle into the air from the launch pad.
1. The height of the rocket when it has traveled horizontally x feet
from the launch pad is given by h = x² x.
A. Graph this equation
x= -b 2a y x 15 25 35 45 55 70 y
200
150
100 50 x

2. B. A 75 ft. tree, 10 ft. from the launch pad, is in the path of the
rocket. Will the rocket clear the top of the tree?
Sec. 9-4

3. 2. The rockets height h at t seconds after launch is given by
h = -22.2t² + 133t .
a. Graph this equation.
b. How high is the
rocket in 2 sec.? x 1 2 3 4 5 6 y y
200
150
100 50 x
Sec. 9-4

4. General Formula for the Height of a Projectile over Time
Let h be the height (in feet) of a projectile
launched with an initial velocity v feet per second
and an initial height of s feet. Then, after t
seconds, h = -16t² + vt + s .
Since 16ft ≈ 4.9 meters, if the units are in meters
in the formula above, then h = -4.9t² + vt + s .

5. 1. A ball is thrown from an initial height of 10 feet with an initial velocity of 64 feet per second.
a. Write an equation describing the height h in feet of the ball after t seconds.
b. How high will the ball be after 3 seconds?
c. What is the maximum height of the ball?

6. 2. An object is dropped from an initial height of 40meters.
a. Write a formula describing the height of the object (in meters)
after t seconds.
b. After how many seconds does the object hit the ground?
c. What is the maximum height of the object?

7. 3. Suppose a ball is thrown upward with an initial upward velocity of 30 meters per second from an initial height of 10 meters.
a Write a formula for the height in meters of the object after t
seconds.
b. Estimate when the ball is 40 meters high.