id: 05945676
dt: j
an: 2011e.00635
au: Madden, Sean P.; Allison, Dean
ti: Pirates of the parametric.
so: Math. Teach. (Reston) 104, No. 9, 666-674 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G74 I24 M54 U64
ut: motion; toys; projectile motion; parabolic trajectories; geometric
concepts; parametric equations; experiments
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=MT2011-05-666a&from=B
ab: Summary: Some children enjoy playing with the spring-loaded, plastic toy
cannon that accompanies many model pirate ships. This cannon pivots in
such a way that it can be fired at any angle from about -15 degrees to
195 degrees when viewed from a position directly in front of the
cannon. The spring provides each fired projectile with approximately
the same initial velocity. This toy, together with a digital camera,
can be used with high school students to demonstrate the influence of
angle on parabolic trajectories and, simultaneously, to explore the
underlying parametric equations. In particular, students can discover
and verify that the vertices of projectile motion paths for a given
initial speed and a range of launch angles trace an ellipse. This
article describes activities that may be tailored by teachers for
students from first-year algebra through calculus. These activities
assume that students are familiar with quadratic functions,
right-triangle trigonometry, and double-angle identities and have some
experience with parametric equations. At the introductory high school
level, students will enjoy collecting the data and will also appreciate
the patterns in the data. However, the teacher will have to tailor the
mathematics to meet the studentsâ€™ level. Many students at the
precalculus and calculus levels will be able to follow a teacher-guided
discussion of the derivation of the parametric equations that describe
the parabolic trajectories. A few students at this level may even be up
to the challenge of deriving these equations themselves, perhaps with
guiding suggestions from the teacher. (Contains 1 table and 5 figures.)
(ERIC)
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