HOMEWORK 17: Quadratic Application Problems
1. If a toy rocket is launched vertically upward from ground level with an initial velocity
of 128 feet per second, then its height h after t seconds is given by the equation:
h(t) = -16t2 + 128t
a. How long will it take for the rocket to return to the ground?
b. After how many seconds will the rocket be 112 feet above the ground?
c. How long will it take the rocket to hit its maximum height?
d. What is the maximum height?
2. You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the
ball. The height that your feet are above the ground is given by the function:
h(t) = -16t2 +12t
a. What is the maximum height your feet will be above the ground?
b. Will you be able to dunk the basketball?
3. One of the games at a carnival involves trying to ring a bell with a ball by hitting a
lever that propels the ball into the air. The height of the ball is modeled by the
equation h(t) = 16t2 + 39t
a. If the bell is 25 ft. above the ground, will it be hit by the ball?
b. What is the highest point the ball reaches?
c. How much time does it take to reach the highest point?
4. A space capsule dives into the water upon re-entry to Earth. The capsule’s path is
represented by the equation H(t)=𝑡 2 − 25𝑡 + 100 where H equals the height of the
capsule in feet, and t is equal to the time elapsed in seconds.
a. When did the capsule enter the water? _____
b. How far underwater did the capsule go? ______
c. When did the capsule exit the water? _____
d. How long was the capsule underwater? _____
e. What was the height of the capsule at 1 second? _____
f. What was the height of the capsule at 10 seconds? _____
5. The graph on the right shows the height h in
feet of a small rocket t seconds after it is
launched. The path of the rocket is given by the
equation: h(t) = -16t2 + 128t.
a. How long is the rocket in the air?
b.
What is the greatest height the rocket
reaches?
c.
About how high is the rocket after 1
second?
After 2 seconds,
d.
about how high is the rocket?
e.
is the rocket going up or going down?
After 6 seconds,
f.
about how high is the rocket?
g. is the rocket going up or going down?