Section 6.3 Parametric Equations and Motion

March 28, 2011

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)

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March 28, 2011

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.

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March 28, 2011

Find a parameterization of the line through
(−3, 1) and (7, 5).

A (7, 5)• 1. → → →

O (0, 0) → →→

B (−•P3,(x1,)•y) 2. → → →
→ → →

→→

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March 28, 2011

Page 531 #46.

Chris and Linda warm up in the outfield by tossing softballs
to each other. Suppose both toss the ball at the same time
from the same height. Find the minimum distance between
the two balls and when this minimum distance occurs.

45 f/s 39° 41 f/s
44° 78 ft (78, 0)

(0, 0)

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March 28, 2011

Page 531 #68.

A 71-ft-radius Ferris wheel turns counterclockwise one
revolution every 20 sec. Tony stands at a point 90 ft to the
right of the base of the wheel. At the instant Matthew is at
point A (3 o'clock), Tony 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 Matthew.

Write parametric equations to
model the flight of the ball.

•

Write parametric equations to
model Matthew's position.

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