What would happen when a jet travelling at Mach 10 experiences engine failure

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NinHursag
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If a hypersonic jet (Mach 10) were to experience sudden engine failure at high altitude what would happen? Would it continue traveling forward, slowly decelerating and descending, thereby giving the pilot chance to attempt a controlled engine restart? Or would the jet experience catastrophic Mach Buffet, drag divergence or Mach Tuck and go into a spin? If such a jet were to experience engine failure while traveling within the mesosphere rather than the stratosphere would this have any effect on the outcome? Thanks.
 
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It would depend on the design of the jet. Depending on a number of things I suppose anyone of your suggestions could occur.
 
Although it "only" traveled at Mach 3, the SR-71 had problems with the engines shutting off during flight. If the flight conditions changed to rapidly for the control system and the shockwave wasn't in the right place it would cause the internal pressure to build up and the engine would shut off. If this only happened to one engine it would create very strong yawing moment and make the aircraft difficult to control.