Math In Basketball Lesson Page 25
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31Answer Key
Math in Basketball: Try other challenges
WHAT IS THE MAXIMUM HEIGHT OF THE BASKETBALL?
6. Plan it out. What strategy will you use? Select one or more representations, such as your
equation or a graph (found on the last page), to calculate the maximum height the ball will
reach on its way to the basket.
Using the value of t, or time, when the ball reaches its maximum height, you can substitute that value into
the equation you set up for h(t) to find the height of the ball at that time, or use graphical representation.
7. Solve your problem. Show all your steps. You may use the graph on the last page of this
handout or show your work in the space below.
See below for all solutions.
ALL FINAL SOLUTIONS:
[h
= Release Height and v
= Initial Vertical Velocity]
0
0
h
= 5’ and v
= 20 ft/sec
0
0
2
h(t) = -16t
+ 20t + 5
At what times (in sec) does the ball reach 10 feet? t = 0.35
t = 0.90
At what time does the ball reach its maximum height?
t = 0.63 (or 5/8 sec)
Maximum height = 11.25 feet
h
= 5’ and v
= 22 ft/sec
0
0
2
h(t) = -16t
+ 22t + 5
At what times (in sec) does the ball reach 10 feet? t = 0.29
t = 1.09
At what time does the ball reach its maximum height?
t = 0.69 (or 11/16 sec)
Maximum height = 12.56 feet
h
= 5’ and v
= 24 ft/sec
0
0
2
h(t) = -16t
+ 24t + 5
At what times (in sec) does the ball reach 10 feet? t = 0.25
t = 1.25
At what time does the ball reach its maximum height?
t = 0.75 (or ¾ sec)
Maximum height = 14 feet
______________________________________________________________________________
h
= 6’ and v
= 20 ft/sec
0
0
2
h(t) = -16t
+ 20t + 6
At what times (in sec) does the ball reach 10 feet? t = 0.25
t = 1.0
At what time does the ball reach its maximum height?
t = 0. 63 (or 5/8 sec)
Maximum height = 12.25 feet
h
= 6’ and v
= 22 ft/sec
0
0
2
h(t) = -16t
+ 22t + 6
At what times (in sec) does the ball reach 10 feet? t = 0.22
t = 1.16
At what time does the ball reach its maximum height?
t = 0. 69 (or 11/16 sec)
Maximum height = 13.56 feet
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