HW Practice Problems for after Part 1 (Punkin’ Chunkin’) of Chapter 9
This problem can be assigned after Ch9 Part 1
This problem can be assigned after Ch9 Part 1
HW# _______ “Football Field Goal”
In football, when a field goal attempt is kicked, it leaves
the ground on a path for which the height of the ball h in
feet at any time t seconds later might be given by a
function like h(t) = 0 + 45t – 16t2.
HW# _______ “Football Field Goal”
In football, when a field goal attempt is kicked, it leaves
the ground on a path for which the height of the ball h in
feet at any time t seconds later might be given by a
function like h(t) = 0 + 45t – 16t2.
a. What does the “0” represent in the equation?
What does the “45t” represent?
What does the “-16t2” represent?
a. What does the “0” represent in the equation?
What does the “45t” represent?
What does the “-16t2” represent?
b. Type the equation into “y=” on your calculator
calculator. Graph it. (Set your WINDOW so that you
can see the graph. You might want to try ZOOM0)
b. Type the equation into “y=” on your calculator
calculator. Graph it. (Set your WINDOW so that you
can see the graph. You might want to try ZOOM0)
c. Make a labeled sketch of the graph. Add the info
that you acquire by doing the following activities.
c. Make a labeled sketch of the graph. Add the info
that you acquire by doing the following activities.
d. Write an equation that tells time(s) when the ball hits
the ground at the end of its flight. Find the time(s)
when the ball hits the ground by using the table on
your calculator. Add this point and label it on the
sketch of your graph.
d. Write an equation that tells time(s) when the ball hits
the ground at the end of its flight. Find the time(s)
when the ball hits the ground by using the table on
your calculator. Add this point and label it on the
sketch of your graph.
e. Write an equation that tells time(s) when the ball is at
the height of the end zone crossbar (10 feet above the
ground). Find the time(s) when the ball is at this
height. Add this point and label it on the sketch of
your graph.
e. Write an equation that tells time(s) when the ball is at
the height of the end zone crossbar (10 feet above the
ground). Find the time(s) when the ball is at this
height. Add this point and label it on the sketch of
your graph.
f. Explain how you could find the maximum height of
kick by using your graph. Explain how you could
find the maximum height of the kick by using the
table. Use either your graph or your table to find
how high the ball is when its at its maximum height
and find when that maximum height occurs. Add
this point and label it on the sketch of your graph.
f. Explain how you could find the maximum height of
kick by using your graph. Explain how you could
find the maximum height of the kick by using the
table. Use either your graph or your table to find
how high the ball is when its at its maximum height
and find when that maximum height occurs. Add
this point and label it on the sketch of your graph.
This problem can be assigned after Ch9 Part 1 and
before “Skydiving”
This problem can be assigned after Ch9 Part 1 and
before “Skydiving”
HW# _______ “Airplane Pumpkin Drop”
Suppose that a pumpkin is dropped from an airplane
flying about 5,280 feet above the ground (one mile up in
the air). The function h(t) = 5280 - 16t2 can be used to
predict the height of that pumpkin at a point t seconds after it
is dropped. But this mathematical model ignores the effects
of air resistance.
HW# _______ “Airplane Pumpkin Drop”
Suppose that a pumpkin is dropped from an airplane
flying about 5,280 feet above the ground (one mile up in
the air). The function h(t) = 5280 - 16t2 can be used to
predict the height of that pumpkin at a point t seconds after it
is dropped. But this mathematical model ignores the effects
of air resistance.
a. How would you expect a height equation that does
account for air resistance to be different from the
equation h(t) = 5280 - 16t2 that ignores air resistance?
We have been exploring the height of the pumpkin over
time for many days. Now you are going to explore the speed
of the falling pumpkin. You are going to explore the speed
with air resistance and without air resistance.
a. How would you expect a height equation that does
account for air resistance to be different from the
equation h(t) = 5280 - 16t2 that ignores air resistance?
We have been exploring the height of the pumpkin over
time for many days. Now you are going to explore the speed
of the falling pumpkin. You are going to explore the speed
with air resistance and without air resistance.
b. The speed of the falling pumpkin at a time t seconds
after it is dropped can be predicted by the function:
b. The speed of the falling pumpkin at a time t seconds
after it is dropped can be predicted by the function:
s1(t)=32t, without air resistance or
s2(t) = 120(1 - 0.74t), with air resistance.
s1(t)=32t, without air resistance or
s2(t) = 120(1 - 0.74t), with air resistance.
i. Enter both equations into your calculator.
(remember… t will be x on the calculator and
s1(t) will be y1 and s2(t) will be y2.)
i. Enter both equations into your calculator.
(remember… t will be x on the calculator and
s1(t) will be y1 and s2(t) will be y2.)
ii. Go to TABLE on your calculator. Write a table for
each of the equations with values from 0 to 10
seconds (0  t  10).
Like this
t
0 1 2 3 4 5 6 7 8 9 10
s1(t)
s2(t)
ii. Go to TABLE on your calculator. Write a table for
each of the equations with values from 0 to 10
seconds (0  t  10).
Like this
t
0 1 2 3 4 5 6 7 8 9 10
s1(t)
s2(t)
iii. Sketch the graphs from your calculator that show
speeds. .(You may want to try ZOOM0). Sketch the
two equations on the same graph.
Label axes and important points.
iii. Sketch the graphs from your calculator that show
speeds. .(You may want to try ZOOM0). Sketch the
two equations on the same graph.
Label axes and important points.
iv. Give similarities and differences in patterns of
change shown by the two (time, speed) equations.
iv. Give similarities and differences in patterns of
change shown by the two (time, speed) equations.
c. Air resistance on the falling pumpkin causes the speed
of descent to approach a limit called terminal velocity.
This is the time when the pumpkin doesn’t fall any faster.
Use your calculator’s table to explore the pattern of
(time, speed) values for the equation s2(t) = 120(1 – 0.74t)
for larger and larger values of t to see if you can discover
the terminal velocity implied by that speed function.
What is that terminal velocity and when does it occur.
c. Air resistance on the falling pumpkin causes the speed
of descent to approach a limit called terminal velocity.
This is the time when the pumpkin doesn’t fall any faster.
Use your calculator’s table to explore the pattern of
(time, speed) values for the equation s2(t) = 120(1 – 0.74t)
for larger and larger values of t to see if you can discover
the terminal velocity implied by that speed function.
What is that terminal velocity and when does it occur.