10.7 Parametric Equations parametric equations: a pair of equations, one for x and one for y, relating both to a third variable t.

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Presentation transcript:

10.7 Parametric Equations parametric equations: a pair of equations, one for x and one for y, relating both to a third variable t.

Example 1: Eliminate the parameter for the curve below:

Example 2: Eliminate the parameter for the curve below:

Projectile Motion When a projectile is in two dimensional motion, the parametric equations for its motion are defined as follows:

Velocity Vector Components If v is the velocity vector with angle θ, then the horizontal and vertical components can be found by the following equations:

Example 3: Jack throws a baseball from 6 ft above the ground with an initial speed of 20 ft/sec at an angle of 35°. How far does the ball travel?

Example 3: To find when the ball hits the ground, we set the second equation equal to zero and solve

What is an alternative way of solving for time in this situation??? Example 3: Since the problem only makes sense if we time starting from t=0 we’ll use the second value in our horizontal distance equation. What is an alternative way of solving for time in this situation???

Example 3: s

10.7 HW Assignment Pg. 694: #s 8-16 evens (eliminate the parameter), 54 (a-d only), 56 (a-d only)