http://www.ck12.org Chapter 10. Polar and Parametric Equations
x 3 =t
y 3 =√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2Now when you graph, you should change your window settings and lettvary between 0 and 4, thexwindow show
between 0 and 4 and theywindow show between 0 and 5. This way it should be clear if the distance truly does get
below 3 feet.
Depending on how accurate yourTste pis, you should find that the distance is below 3 feet. Kieran does indeed catch
the ball.
Concept Problem Revisited
The parametric equations for the point on the wheel are:
x=20 sin(π
30 t)
y=−20 cos(π
30 t)
+ 26
The horizontal parameterization is found by noticing that thexvalues start at 0, go up to 20, go back to 0, then down
to -20, and finally back to 0. This is a+sin pattern with amplitude 20. The period is the same as with the vertical
component.
Vocabulary
A calculator can reference internal variableslikex 1 ,y 1 that have already been set in the calculator’s memory to
form new variables likex 3 ,y 3.
Thehorizontal and vertical componentsof parametric equations are thex=andy=functions respectively.
Guided Practice
- At what velocity does a football need to be thrown at a 45◦angle in order to make it all the way across a football
field? - Suppose Danny stands at the point (300, 0) and launches a football at 67 mph at an angle of 45◦towards Johnny
who is at the origin. Suppose Johnny also throws a football towards Danny at 60 mph at an angle of 50◦at the exact
same moment. There is a 4 mph breeze in Johnny’s favor. Do the balls collide in midair? - Nikki got on a Ferris wheel ten seconds ago. She started 2 feet off the ground at the lowest point of the
wheel and will make a complete cycle in four minutes. The ride reaches a maximum height of 98 feet and spins