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Example Problem: What is the Mach number of a plane if the speed of sound is 761 mph and the plane is traveling at 500. mph? Classify this high-speed flight as subsonic, transonic, supersonic, or hypersonic. Solution: The Mach number is defined as the following ratio: speed of object . Mach number = 500. mph speed of sound 761 mph = 0.657 This airplane is traveling at a subsonic speed. PROBLEMS 1. For each statement below, say something about the relationship between a and b if their ratio = ab. Ratios If the ratio is equal to 1.0, then If the ratio is less than 1.0, then If the ratio is greater than 1.0, then If the ratio is nearly zero, then If the ratio is very large, then __________________________. __________________________. __________________________. __________________________. __________________________. 2. A typical cruise speed of a Boeing 757 is Mach 0.800. What is the typical cruise speed (in miles per hour) of a Boeing 757 if the speed of sound at cruise altitude is 760. mph? 3. What is the thrust-to-weight ratio of a Boeing 747 (m = 174,000 kg) when a thrust of 215,000 N is generated? 4. What is the wingspan and wing area of a Boeing 757? What is the aspect ratio of a Boeing 757? (Use the Internet to obtain the necessary data.) 5. (Optional) Visit the Web page in the Introduction, and write a description on one of the ratios not previously mentioned in this section. Then create a word problem dealing with this ratio. Also include the solution. 60PDF Image | NASA Guide to Engines
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