February 27, 2012
Section 6.3 Parametric Equations and Motion
A parametric curve is the graph of the ordered
pairs (x, y) where
are
functions defined on an interval I of t-values.
The equations
are
parametric equations for the curve and the
variable t is a parameter, and I is the parameter
interval.
Eliminate the parameter if
a)
b)
February 27, 2012
What pair of parametric equations represent
the unit circle?
What is the smallest interval of values for
t needed to graph a complete circle?
What is the resulting graph if the t-step is
Find a parametrization of the circle with
center (−2, −1) and radius 5.
x = -2 + 5cos T
y = -1 + 5sin T
February 27, 2012
Find a parameterization of the line through
(−3, 1) and (7, 5).
A (7, 5)
•
1.
→
→
→
→
→
→
2.
→
→
→
→
→
→
B (−3, 1)
•
•P (x, y)
O (0, 0)
→
→
February 27, 2012
Page 531 #46.
LJ and Charly warm up in the outfield by tossing baseballs
to each other. Suppose both toss a ball at the same time from
the same height. Find the minimum distance between the
two balls and when this minimum distance occurs.
45
(0, 0)
f/s
44°
39°
78 ft
41 f
/s
(78, 0)
February 27, 2012
Page 531 #68.
A 71-ft-radius Ferris wheel turns counterclockwise
one revolution every 20 sec. Joey stands at a point 90
ft to the right of the base of the wheel. At the
instant Andy is at point A (3 o'clock), Joey throws a
ball toward the Ferris wheel with an initial velocity of
88 ft/sec at an angle with the horizontal of 100°. Find
the minimum distance between the ball and Andy.
Write parametric equations to
model the flight of the ball.
•
•
A
•
Write parametric equations to
model Matthew's position.