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Unit 8, Modeling Motion using Parametric Equations with Answers
Blackline Masters, Advanced Math – Pre-Calculus
Page
Louisiana Comprehensive Curriculum, Revised 2008
267
1. A skateboarder goes off a ramp at a speed of 15.6 meters per second. The angle of
elevation of the ramp is 13.5
, and the ramp's height above the ground is 1.57 meters.
a) Give the set of parametric equations for the skater's jump.
a)
xt
y
t
t
t
t
oo
==
−
+
+
=−
+
+
(.c
o
s.)
(
.
)
(.s
i
n.) .
..
.
.
156
135
1
2
98
157
152
4 9
364
2
2
and
and y =
b) Find the horizontal distance along the ground from the ramp to the point he
lands.
He will land when y = 0. y = 0 when t = 0.954
then x = 15.2(0.954) = 14.5 meters
2. A baseball player hits a fastball at 146.67 ft/sec (100 mph) from shoulder height (5
feet) at an angle of inclination 15
o
to the horizontal.
a) Write parametric equations to model the path of the project.
yt
t
o
o
=
+
(.
c
o
s)
_(
.
sin
)
146 67
15
16
146 67
15
5
2
b) A fence 10 feet high is 400 feet away. Does the ball clear the fence?

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