Greenwood press
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book-20600
- Bu sahifa navigatsiya:
- Triangle Trigonometry
- Proportions
104
RATIO water. But when the plane hits the speed of sound, the airwaves can’t move out of the way of the plane. The build up at the front of the plane causes a shock wave that creates stress on the plane and is often audible to people on the ground as a “sonic boom.” The speed of sound varies according to temperature and other factors. It is about 762 miles per hour at sea level, and about 664 miles per hour at 35,000 feet. A jet traveling at 1,400 miles per hour 35,000 feet above sea level would be traveling at 1400/664 ≈ Mach 2.1. A jet-propelled wheeled vehicle achieved Mach 1.02 on the Bonneville Salt Flats on a day when the speed of sound was 748 mph. Its speed was 763 miles per hour. Astronomers measure solar-system distances with a ratio measure called an astronomical unit (AU). An AU of 1 represents the average distance of the earth to the sun, about 14,960,000,000 kilometers. For even larger distances than the solar system (which is about 80 AU in diameter), astronomers use ratio measures based on light years. One light year is the distance traveled by light in one year (about 9.46 × 10 17 cm). Our galaxy is about 100,000 light years in diameter. Par- secs (3.26 light years), kiloparsecs (1,000 parsecs), and megaparsecs (1 million parsec) are used to measure distances across many galaxies. Trigonometric ratios are used to find unusual or inaccessible heights and lengths. By measuring angles and shorter distances, an engineer can calculate the height of skyscrapers by creating diagrams with right triangles and using these ratios. (See Triangle Trigonometry for an explanation.) Scale models use ratios to indicate how the lengths of an object compare to corresponding measures in the model. A 1:29 scale-model train would be large enough for children to ride outdoors on top of the cars. It would be 1/29th of the size of a real train. An HO-gauge tabletop train is at a scale of about 1:87. An 8.64-inch model of an 18-foot-long automobile (216 inches) would be at the scale of 1:25. Scale models can also help provide information to calculate unknown information, such as the mass of a dinosaur. (See Similarity.) Although the design of buildings, cars, toasters, and furniture may involve drawings and models that are smaller than the final version, scale models that are larger than real life are important in many fields. Manufacturers of computer chips make scale drawings much larger than the actual chip to show the packed circuitry. Medical researchers make large-scale models of viruses and cell structures to determine how shapes affect resistance to disease. The fundamental law of similarity uses scaling to indicate how surface area and volume of the model relate to the actual object. If k is the ratio of a length in the object to the corresponding length in the model, k 2 is the ratio of surface areas, and k 3 is the ratio of volumes. This law explains the limits on human and animal growth. If a six-foot-tall, 180-pound human were to double in size so that his relative proportions were maintained, he would be twelve feet tall, but his volume, and hence his weight, would be eight times as much. The giant’s weight would be 1,440 pounds—which couldn’t be supported by human bone structures. (See Proportions for an alternate explanation.) Download 1.81 Mb. Do'stlaringiz bilan baham: |
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