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NSTRUMENTS
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31
Activity 5—Rolling ball
(cont.)
parabolic
Explorations
Examine what happens for differing inclines.
➊
Predict what will happen if the incline increases.
Answer question 6.
➋
Adjust the incline to 30
¡
. Repeat steps 2 through 6.
Add this plot to the drawing in
question 6, labeled
30
¡
.
➌
Repeat steps 2 through 6 for inclines of 45
¡
and 60
¡
and add to the drawing.
➍
Answer question 7.
Advanced explorations
Adjust the time values so that x = 0 for the initial height (the time at which the ball was
released. You can do this manually by subtracting the x value for the first point from all the
points on your plot, or you can enter
L1(1)
"
A:L1
N
A
"
L1
.
➊
Calculate the values for
a
,
b
, and
c
for the family of curves in the form
y = ax
2
+ bx + c
at 0
¡
, 15
¡
, 30
¡
, 45
¡
, 60
¡
, 90
¡
.
➋
What are the minimum and maximum values for
a
? Why?
➌
Write an expression describing the mathematical relationship between
a
and the angle
of inclination.
