Parametric Equations for Moving Objects

Property: Parametric Equations of a Cycloid

x = a(t-sint)
y = a(1-cost)

t is the number of radians the wheel has rolled so far
a is the radius

Objective : Be able to find the parametric equations for the path of a moving object.
Here is a example to explain how to do this:

An airplane is flying to LA from Nevada at a speed of 400 mi/hr. It is at point (20,30) on a Cartesian plane at t = 0 hr. LA is the origin. There are two winds going in different directions blowing. The wind blowing south is moving at a velocity of 90 mi/hr. The wind blowing west is moving at a velocity of 120 mi/hr.

Find the parametric equations for the airplane's path. Use t as hours.

x=20-120t
Since the original point of the plane is (20,30) and the velocity of the force blowing horizontally is 120mi/hr, x = the orignial x value + distance (which is rate x time)
In the same way
y=30-90t
The distance is negative becuase the wind is blowing in the negative directions of x and y.

Predict how long it will take for the plane to be 5 miles north of LA.
First plug 5 in for y.
5=30+90t
t=1.66666667
It would take 1.667 hours to get to this point.

try this site for more help: http://www.assembleme.com/post_2004_07_22_parametric_equations.pdf

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