Quadratic Word Problems
Chapter: 2 Assign: 4
If you want credit, show your work and write your answers on a separate sheet of paper. Leave your
answers as decimal approximations.
1. In winter with heavy snow, the animals in Yellowstone cannot freely roam to find food, so hay is
dropped for them from helicopters. A helicopter is 180 feet above the ground drops a bale of hay while
the helicopter itself is rising at 32 feet per second. The height (S) in feet of the bale as a function of
time is given by:
S(t) = −16t 2 + vit + Si
where t is the time since the bale was dropped off the helicopters (in seconds), vi is the initial velocity,
and Si is the initial height.
a. What is the height of the bale 2 seconds after it is released?
b. How many seconds will it take the bale to reach the ground?
c. When does the bale reach its maximum height? What is the maximum height?
d. Sketch and label a graph of the height of the bale as a function of time. Explain the shape of the
graph.
2. A motorcycle stunt rider jumped across the Snake River. The path of the motorcycle was given
approximately by:
S(t) = −.0005t 2 + 2.39t + 600
Where S(t) is the height, measured in feet, above the top of the canyon and t is the horizontal distance
from the launch ramp, in feet.
a. What was the rider's maximum height above the canyon?
b. How far (horizontal distance) was the rider from the ramp when she reached her maximum height?
c. How high above the canyon was the launch ramp?
3. A tomato is thrown vertically into the air at time, t=0. Its height, d (in feet), above the ground at time
t (in seconds) is given by:
d(t ) = −16t 2 + 48t
a. Find t, when d(t)=0.
b. What is happening to the tomato the first time d(t)=0? What is happening the second time?
c. When does the tomato reach its maximum height?
d. What is its maximum height?
e. Sketch a graph of d(t)
4. A football is kicked. The height of the ball, h in feet, as a function of the horizontal distance
traveled, d in feet, is given by:
h(d) = .75d − .01914d 2
a. When the ball hits the ground, how far away is it from the spot where the football player kicked it?
b. What is the maximum height the ball reached during its flight?
c. What is the horizontal distance the ball has traveled when it reaches its maximum height?
d. Sketch the graph of h(d).
5. A homeowner wishes to enclose a small rectangular area with 25 feet of fencing for use as a flower
garden. One side of the garden will be against the house, so there is no need to put fencing along that
side. What dimensions should be used in order to maximize the area of the garden? What is that
maximum area?
6. Two people are playing table tennis. The height of the ball above the table is given by
2
where h stands for the height in meters and t stands for time in seconds.
h(t) = −4.9t + 2.1t
a. Find the maximum height the tennis ball reaches.
b. How much time has gone by when the ball reached that height?
€
2
7. Janet threw a basketball. The equation h(t) = −16t + 5t + 5 describes the height h of the ball in t
seconds after she threw it.
a. How many seconds passed before the ball hit the ground?
b. How long did it take for the ball to reach its maximum height?
€
8. A tennis player practices lobs. The height of the ball above the ground is given by
h(t) = −16t 2 + 20t + 5 where h is the height in feet and t is the time in seconds.
a. How far above the ground is the ball when she first hit it?
b. What is the maximum height the ball reaches?
c. How long does it take for the ball to hit the ground?
€
2
9. The equation d(s) = .0056s + .14s models the relationship between a vehicle's stopping
distance, d, in meters and the vehicle's speed, s, in kilometers per hour. If a driver is traveling at 130
kph, what distance should the driver leave between the drive's car and the car in front of it?
10. A€ball is thrown from a building 30 feet tall. The height, h, of the ball above the ground t seconds
2
after it is dropped is modeled by the equation h(t) = −4.9t + 2.8t + 35
a. How long will it take the ball to reach the ground?
b. How high is the ball after 1.5 seconds?
11. An experiment shows that the relationship
between a time t that it takes a person to react to a sound
€
2
and a person's age, a, in years can be modeled by the equation t = .0051a − .3185a + 15.0008
a. How long would it take for a 16 year old to react?
b. How long would it take a 44 year old to react?
12. A model rocket is fired into the air. The height,€h, in feet, of the rocket above the ground t, seconds
2
after launching is given by h = 80t −16t
a. Find the maximum height of the rocket.
b. How long does it take the rocket to reach this height?
c. How long does it take the rocket to reach the ground?
€