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44. A right cone sliced vertically through its vertex results in a triangle. (An isosceles triangle, actually.) This could be considered a degenerate hyperbola. A horizontal cut makes a circle.45. A flashlight with a single bulb and mirror backing should illuminate an approximately cone-shaped volume when projected onto a flat surface, as long as there are no significant asymmetries in the bulb, filament, or mirror. The various conic sections can be projected on a wall by holding the light at different angles, resulting in what is essentially a “cut” through the illuminated cone of light.Lesson 5(MATHEMATICS)Teacher Resource 2Problems on Conic Sections — Answer Sheet38. The same calculation as in the previous problem gives an eccentricity of 0.207.39. The orbit of Halley’s comet is a highly elongated ellipse.40. This mini-research project is a good opportunity to discuss what scientists actually do. In particular, be sure to point out the absolute distinction between “a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena” and idle “speculation” (as defined by Merriam-Webster). These are almost opposite meanings of the same word. Unfortunately, confusion between the two has led many who should know better to apply the unfortunate phrase “just a theory” to well-established scientific theories.41. Another good mini-research project that makes a good homework assignment. Of particular interest was the fact that in deriving his laws, Kepler made use mostly of data collected by Tycho Brahe. Brahe advocated a model in which the sun orbited the Earth, but the other known planets orbited the sun. Also interesting is that Brahe collected all his data without the use of a telescope.
Journeys in Film: Hidden Figures46. An object that “falls” toward a star or planet at a very high speed will swing around the star or planet once, and continue outward, never to return again, as long as there is no collision. This type of orbit is hyperbolic. Some comets behave this way. Do a search for “hyperbolic comets” for more details.47a. approximately circular47b.highly elliptical47c. approximately parabolic47d. parabolic at launch and return, approximately circular during its orbit47e. hypothesized to have had a roughly circular orbit in the asteroid belt, but became increasingly eccentric through gravitational perturbations. This happened to put it in the path of Earth.47f.hyperbolic relative to Jupiter47g. highly elliptical47h. hyperbolic (It will leave the solar system.)Lesson 5(MATHEMATICS)Teacher Resource 2Problems on Conic Sections — Answer Sheet
96Journeys in Film: Hidden Figures
97Journeys in Film: Hidden FiguresLesson 6(PHYSICS, PROGRAMMING)Computers Come of AgeEnduring Understandings• A nonzero net force on an object causes a change in its momentum. (Newton’s second law)• Newton’s laws apply at vastly different scales.