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Unit 8, Activity 6, Modeling Motion using Parametric Equations
Blackline Masters, Advanced Math – Pre-Calculus
Page
Louisiana Comprehensive Curriculum, Revised 2008
265
Part III.
1. Consider two objects in motion over the time interval 0
≤
t
≤
2
π
.
The position of the
first object is described by the parametric equations
xt
t
1
23
=
=
cos
sin
and y
1
.
The
position of the second object is described by the parametric equations
t
2
13
=+
−
sin
cos
and
.
At what times do they collide?
Set
2
1
x
x
=
and
2
1
y
y
=
and solve the resulting system of equations.
The objects
collide when t =
2
3
π
.
This occurs at the point (0, -3). Graphing the two
parametric equations shows another point of intersection but it is not a point of

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