Activity 15.7.1 – Scientific and technological examples of conic sections
The following is a list of the practical applications of conic sections (circle, parabola, ellipse, and hyperbola) or their three dimensional rotations (sphere, paraboloid, ellipsoid, and hyperboloid). Identify each of the following as a circle, parabola, ellipse, hyperbola, sphere, paraboloid, ellipsoid, or hyperboloid.
- The celestial equator is a _____________ projection into space of the Earth’s equator. Astronomers use the celestial equator to reference the position of stars and other celestial objects.
- If a source of sound is placed at one focus of an _________ room, the sound converges on the other focus. For this reason, concert halls do not have this shape.
- Loran is an acronym for Long Range Navigation, a technology developed during World War II to identify the location of ships at sea. Two transmitters (A1, A2) beam radio signals from fixed points at land. Upon analyzing the time difference between the two signals, the onboard Loran system determines the specific __________ curve on which the boat must be located (figure 15.5D). This process is repeated with a different set of transmitters (B1, B2), and the intersection of the resulting _________ curves identifies the boat’s precise location.
- The “high beam” lamp in an automobile headlight is placed at the focus of a ___________ reflecting surface, such that the emanating light reflects off the curved surface and leaves in parallel rays, lighting the distant road.
- The Moon orbits the Earth in an __________ path with the Earth at one focus.
- The International Space Station and other artificial satellites travel in ___________ orbits with the Earth at one focus.
- A free-throw in basketball, a line-drive in baseball, or a long-bomb in football all follow a ____________ path (neglecting air friction).
- A returning comet follows a highly eccentric __________ path with the Sun at one focus. As the comet approaches perihelion (the closest it gets to the Sun), solar winds (high energy particles from the Sun) lengthen the tail of the comet, and sunlight illuminates it, making it long and visible. As the comet approaches the other focus deep in the Solar System, the tail shrinks and the comet becomes invisible to the Earth-bound observer.
- To intensify the light from faint, distant objects, ___________ telescope mirrors collect and focus parallel beams of light.
- Water from a hose, sprinkler, drinking fountain, or decorative fountain travels in a ____________.
- Sportscasters eavesdrop on the conversations of coaches and players by using microphones placed at the focus of ___________ reflectors.
- The Le Four Solaire et Font-Romeur is an 8-story high _________ solar reflector in the mountains of France. It is made of 8000 mirrors arranged so that light reflects to one focus, generating temperatures up to 6000 degrees Fahrenheit.
- To create a weightless condition, NASA flies training astronauts in planes with an upward ________ trajectory. Using this technique, astronauts can train in a weightless environment for approximately 30 seconds at a time.
- The light cast on a wall, above and below a lampshade forms a ___________ .
- Three lobed ___________ cylinders are used to concentrate light at a common focus.
- In the absence of gravity, bubbles, water droplets, and flames assume a __________ shape.
- Although the Earth appears to be a sphere, it is actually more nearly an ____________. The flattening of the ellipse of the Earth is only about one part in three hundred, but is significant enough to become a necessary part of calculations in plotting accurate maps at a scale of 1:100,000 or greater.
- When a rock is thrown in a pond it generates ____________ surface waves.
- The surface waves from an Earthquake expand in a _____________ fashion.
- A ______________ ball and socket joint allows for rotary motion.
- The __________ radiocarpal joint in the wrist allows front-back movement along the short axis, but limited movement along the long axis.
- The curve of cables in a suspension bridge form a _______.
- When two rocks are dropped in the water at the same time, they create radiating rings. When the peak of one wave hits the peak of another, the wave doubles in height, but when the peak of one hits the trough of another, the waves cancel. These patterns of constructive and destructive interference form a __________.
- Microwave antennae are _________ and can therefore collect and concentrate signals at the focus.
- The heating element of a radiant heater is placed at the focus of a __________ such that the infrared rays will project evenly and warm the room in which it is placed.
Answers (roll over to see)
15.7.1 (1) circular, (2) elliptical, (3) hyperbolic, (4) parabolic, (5) elliptical, (6) elliptical, (7) parabolic, (8) elliptical, (9) parabolic, (10) parabolic, (11) parabolic, (12) parabolic, (13) parabolic, (14) hyperbola, (15) elliptical, (16) spherical, (17) ellipsoid, (18) circular, (19) circular, (20) spherical, (21) ellipsoid, (22) parabola, (23) hyperbola, (24) parabolic, (25) parabola.