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# Unless indicated otherwise, assume the speed of | Ch 16 - 56E ISBN: 9780321675460 31

## Solution for problem 56E Chapter 16

University Physics | 13th Edition

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Problem 56E

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0o with its direction of motion. The speed of sound at this altitude is 331 m/s. (a) What is the Mach number of the shuttle at this instant, and (b) how fast (in m/s and in mi/h) is it traveling relative to the atmosphere? (c) What would be its Mach number and the angle of its shock-wave cone if it flew at the same speed but at low altitude where the speed of sound is 344 m/s?

Step-by-Step Solution:

Solution 56E Step 1: a) Since it is making an angle with the cone, we can write, sin = v/v spaceship The equation for the Mach number, M = u/v u - local flow velocity v - speed of sound But, here, u = v spaceship v = 331 m/s at highest altitude Therefore, we can write, v spaceshipv / sin from the first equation. That is, v spaceship31 m/s / sin 58 = 331 m/s / 0.8480 vspaceship90.33 m/s Therefore, Mach number, M = 390.33 m/s / 331 m/s = 1.179 Step 2: b) The speed of the spaceship is = 390.33 m/s We know that, 1 s = 1/3600 hr 1 m = 1/1000 km Therefore, 1 m/s = (1/1000) km / (1/3600) hr = 18 /5 km/hr Substituting this and converting the units we get, vspaceship 90.33 × (18/5) km/hr = 1405.19 km/hr km = 1.61 miles Therefore, v spaceship(1405.19 /1.61) miles / hour = 872.79 mph

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##### ISBN: 9780321675460

The answer to “Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0o with its direction of motion. The speed of sound at this altitude is 331 m/s. (a) What is the Mach number of the shuttle at this instant, and (b) how fast (in m/s and in mi/h) is it traveling relative to the atmosphere? (c) What would be its Mach number and the angle of its shock-wave cone if it flew at the same speed but at low altitude where the speed of sound is 344 m/s?” is broken down into a number of easy to follow steps, and 114 words. Since the solution to 56E from 16 chapter was answered, more than 239 students have viewed the full step-by-step answer. This full solution covers the following key subjects: speed, its, Sound, mach, Atmosphere. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 56E from chapter: 16 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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