Chapter 5 Word Problems
Name: __________________________
An object that is launched, thrown, or dropped, can be modeled by the function:
h = -16t2 + v0t + h0
where h is the height (in feet) of the object after t seconds, t is the time in seconds, v0
is the initial velocity, and h0 is the object’s initial height in feet.
Initial velocity can be …
positive 1)
negative -
zero –
A stunt man working on a set of a movie is to fall out of a window 200 feet above
the ground.
a. What is the equation for this example?
b. How high will the stunt man be after .5 seconds? 2 seconds?
c. How much time will it take him to reach a height of 64 feet?
d. When will the man hit a rectangular cushion that is 10 feet above the ground?
e. What is the proper domain for this function? The proper range?
f.
Graph the function:
2) From 32 feet above the ground, Julie shoots an arrow upward with a
velocity of 64 feet per second.
a) Write the equation that models this scenario.
b) Find the height of the arrow 3 seconds after it was shot?
c) Find the maximum height reached by the arrow and the time that
this height is reached.
d) Then find the total time the arrow is in the air.
e) When will the arrow reach a height of 80 feet?
f) Write the equation in vertex form.
3)
At an engineering school, students are challenged to design a container that
prevents an egg from breaking when dropped from a height of 50 feet. Write an
equation giving a container’s height h (in feet) above the ground after t seconds.
Write an equation representing the situation and determine how long it will take
for the container to hit the ground?
4)
A baton twirler tosses a baton into the air. The baton leaves the twirler’s hand 6
feet above the ground has an initial velocity of 45 feet per second.
a. What is the equation?
b. What is the highest point that the baton will go?
c. The twirler catches the baton when it falls back to a height of 5 feet. How
long is the baton in the air?
5)
Eric was considering joining the circus and was practicing juggling while standing
on the top of a 10 foot ladder. He was using tennis balls and threw each ball
upward at a speed of 8 feet per second. Find the maximum height reached by one
of the balls and the time this height is reached.
6) A flare is launched from a life raft with an initial vertical velocity of 192 feet per
second. When is the flare 512 feet above the raft?
7) A toy rocket is fired in the middle of a field with an initial vertical velocity of 256 feet
per second. When will the rocket land in the field?
8) Another rocket is launched with an initial vertical velocity of 128 feet per second.
What is the maximum height the rocket with reach?
9) The Tower of the Americas in San Antonio, Texas, was built for the 1968 World’s Fair.
At 750 feet it is taller than both the Washington Monument in Washington, DC and
the Space Needle in Seattle, Washington.
Part 1: When visiting her brother, Mrs. Klotz decided to drop a penny from the top
of the Tower of the Americas.
a) At about what time will the penny be 100 feet above the ground?
b) How long will it take for the penny to reach the ground?
Part 2: To celebrate her brother getting married, Mrs. Klotz launched a fireworks
display from the Tower of the Americas. If the fireworks were launched with an
initial vertical velocity of 64 feet per second, when will the fireworks reach the
ground?