44 a right cone sliced vertically through its vertex

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 2
Problems on Conic Sections —
Answer Sheet
38. 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 Figures
46. 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.
47 a . approximately circular
47 b . highly elliptical
47 c . approximately parabolic
47
d
.
parabolic at launch and return, approximately
circular during its orbit
47 e . 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.
47 f . hyperbolic relative to Jupiter
47 g . highly elliptical
47
h
.
hyperbolic (It will leave the solar system.)
Lesson 5
(MATHEMATICS)
Teacher Resource 2
Problems on Conic Sections —
Answer Sheet

96
Journeys in Film : Hidden Figures

97
Journeys in Film : Hidden Figures
Lesson 6
(PHYSICS, PROGRAMMING)
Computers Come of Age
Enduring 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.