Miranda throws a set of keys up to her brother, who is
standing on a third-story balcony with his hands 38 ft above
the ground. If Miranda throws the key with an initial velocity
of 40 feet per second, the equation h = 5 + 40t - 16t2 gives the
height h of the keys after t seconds.
1. How high do the keys reach?
30 ft
2. Will her brother be able to catch the keys or not, explain?
No, he’s taller than the highest point.
The opening of the cannon is 16 feet above the ground. The
daredevil, who is shot out of the cannon, reaches a maximum
height of 55 feet after about 1.56 seconds and hits a net that is
9.5 feet off the ground after 3.25 seconds. Use this
information to answer the following questions.
1. Write a rule that relates the daredevil’s height above the
ground h at a time t seconds after the cannon is fired.
H = 16 + 50t-16t2
2. At what upward velocity is the daredevil shot from the
cannon?
50 ft/sec
3. If, for some unfortunate reason, the net slipped to the
ground at the firing of the cannon, when would the
daredevil hit the ground?
3.42 seconds
From the height of 256 feet above a lake on a cliff, Mikaela
throws a rock out over the lake. The height H of the rock t
seconds after Mikaela throws it is represented by the equation
H = 256 + 32t – 16t2.
1. What does the number 256 represent in the equation?
The height the rock is thrown
2. What does the number 32 represent in the equation?
The speed the rock is thrown
3. To the nearest tenth of a second, how long does it take
the rock to reach the lake below?
5.1 seconds
Katie, a goalie for Enloe High School’s soccer team, needs to
get the ball downfield to her teammates on the offensive end
of the field. She punts the ball from a point 2 feet above the
ground with an initial upward velocity of 40 feet per second.
1. Write a function rule that relates the ball’s height above
the field h to its time in the air t.
H = 2 + 40 t – 16t2
2. Use this function rule to estimate the time when the ball
will hit the ground.
2.55 seconds
A first-time diver was a bit nervous about his first dive at a
swimming pool. To ease his worries about hitting the water
after a fall of 15 feet, he decided to push a tennis ball off the
edge of the platform to see the effect of landing in the water.
1. What rule shows how the ball’s height above the water h
is related to elapsed time in the dive t?
H = -16t2+15
2. Estimate how long it will take the ball to hit the water.
.97
For a typical basketball shot, the ball’s height (in feet) will be a
function of time in flight (in seconds), modeled by an equation
such as h = 6 + 40t -16t2.
1. Assuming that nobody touches the ball before it hits the
floor, what is the maximum height of the shot and at what
time will it occur? Show your work or explain your
reasoning.
Maximum height of 31 feet occurs 1.3 seconds after the
ball is shot
2. When will the ball hit the floor, if it missed the basket
entirely?
2.66
When launching fruit at the state contest, the goal is long
distance, not height. Suppose the relationship between
horizontal distance d (in feet) and time t (in seconds) is given
by the function rule d = 70t, when the height is given by
h = 20 +50t-16t2
1. How long will the fruit be in the air?
3.48
2. How far will the fruit travel from the chunker by the time it
hits the ground?
243.6
The function rule h = 2+40t – 16t2 describes a quadratic
function.
1. What does the number 2 represent in the equation?
Initial Height
2. What does the number 40 represent in the equation?
Velocity
3. Write a story that matches this scenario.
Blah
4. When will this object hit the ground?
2.54