Parametric Equations
Parametric Equations
The Spider and the Fly
A spider and a fly crawl so that their positions at time t (in seconds) are:
Spider: x1 = -2 + t, y1 = 5 - 2t Fly: x2 = 1 - t, y2 = 1 + t
Put your calculator in parametric and simultaneous mode and type in the parametric equations.
Window: T min = 0 X min = -6 Y min = -6
T max = 10 X max = 6 Y max = 6
T step = 1 X scl = 1 Y scl = 1
(a) At what point do their paths cross? (use the trace button to help you)
(b) Do their paths cross at the same time? (to slow up the graphing change T step to .1)
Check the table entries.
(c) Use algebra to show if the paths cross at the same time. (hint: set x1 = x2 and find t.
set y1 = y2 and find t. Do the t’s match?)
Football
From a point 90 feet directly in front of the goal posts with the crossbar 10 feet above the ground, a football is kicked at an angle of elevation [pic] with the ground and with initial velocity [pic]. If a coordinate system is set up with the ball at (0, 0) then the position (x, y) of the ball t seconds after it is kicked
is given by the parametric equations:
[pic] and [pic]
Suppose the initial velocity of the ball is 60 ft/sec
and the angle of elevation is[pic].
Put your calculator in degree, parametric and sequential modes.
To graph the goal post: x1 = 90, y1 = t
To graph the path of the ball: x2 = (60cos30)t, y2 = (60sin30)t – 16t2 (use the -0 next to x2)
Window: T min = 0 X min = 0 Y min = 0
T max = 10 X max = 100 Y max = 20
T step = 1 X scl = 1 Y scl = 1
To get a “better” picture change T step to .1
(a) Does the ball clear the crossbar on the goal posts?
(b) Keep v = 60 ft/sec and change the angle. What is the smallest angle (to the nearest whole)
that will allow the ball to pass over the crossbar?
Cool Graphs
(1) radian mode: x1 = cos(3t), y1 = sin(3t)
Window: T min = 0 X min = -1 Y min = -1
T max = 10 X max = 1 Y max = 1
T step = 1 X scl = 1 Y scl = 1
Now, try changing T step to .1
(2) x1 = cos(3t), y1 = sin(5t)
Same window
What a difference!
=============================================================================
(1) Spider and fly:
Spider: x1 = 3 + 2t, y1 = -2 + t Fly: x2 = -1 + 4t, y2 = 6 - 3t
Do parts (a), (b), (c)
(2) Football:
Change [pic] to 58 ft/sec
Do parts (a) and (b)
(3) If you can find a “cool” parametric graph,
give the equations and window.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- parametric equations derivative
- parametric equations in rectangular form
- parametric equations of a circle
- parametric equations precalculus
- parametric equations calculator with points
- vector and parametric equations calculator
- parametric equations from two points
- find parametric equations calculator
- 3d parametric equations calculator
- graphing parametric equations 3d
- parametric equations grapher 3d
- parametric equations examples with answers