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Hypersonic scramjet. On March $27,2004,$ the United States successfully tested the hypersonic $\mathrm{X}-43 \mathrm{A}$ scramjet, which flew at Mach 7 (seven times the speed of sound) for 11 seconds. (A scramjet gets its oxygen directly from the air, rather than from fuel.) (a) At this rate, how many minutes would it take such a scramjet to carry passengers the approximately 5000 $\mathrm{km}$ from San Francisco to New York? (Use 331 $\mathrm{m} / \mathrm{s}$ for the speed of sound in air.) (b) How many kilometers did the scramjet travel during its 11 second test?

a) $36 \mathrm{min}$ b)$25.5 \mathrm{km}$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

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so, essentially, if it reached Mach seven, how long would it take to complete the round trip to San Francisco? So for party, we can say that D equals the velocity, times, time The distance equals velocity, times time. So we can say that the time equals the distance divided by the velocity. And this is going to be equal to 5.0 times 10 to the sixth meters and then divided by seven times mock. And the speed of sound is 331 meters per second. So seven times 331 and we're getting that the time is going to be 2,158 seconds. We can multiply this by one minute for every 60 seconds. And we're getting approximately 36 minutes now for part B that the question is asking us. How long does it how fast? How far does a travel during this 11 2nd test? So we have the distance equals velocity, times, time, the velocities again, seven times the speed of sound, and then the time would be the test run of 11 seconds. And this is giving us 25,487 meters. We can round and say simply 25.5 kilometers. So during 11 seconds it already travels 25.5 kilometers and it would take again 36 minutes to complete that round trip to San Francisco. That is the end of the solution. Thank you for watching.

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