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Real Conics Applications
Name: Christine
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
I tutor a 10th grade student in honors algebra 2 and he
has been asked to find real world equations involving conic sections
in non-standard form. The purpose of this is for him to be able to
rewrite the equations in standard form and find all related info
(foci, vertex, etc) from the equations while at the same time seeing
that math is used in the world around us. Please send any equations
and tell where they are used.
Replies:
Christine,
One such example is a rolling wave on the ocean surfaces. The water
doesn't travel with the waves. The water moves both up-and-down and
back-and-forth. The vertical motion, as a function of time, is
sinusoidal: y=(y_0)*sin(w*t). The horizontal motion is also
sinusoidal, but out of phase with the vertical motion:
x=(x_0)*cos(w*t). x_0 and y_0 are constants, the horizontal and
vertical amplitudes. w is the angular frequency, a constant often
measured in radians per second. t is time, a variable representing the
passage of time. As time passes, the water often moves in an elliptical
pattern when viewed from the side. If the amplitudes are equal, the
pattern is circular.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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Update: June 2012
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