A space probe enters the thin atmosphere of a planet where the speed of sound is only about 42 m/s.
- What is the probe’s Mach number if its initial speed is 15,000 km/h?
- What is the angle of the shock wave relative to the direction of motion?
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This is Giancoli Answers with Mr. Dychko. Mach number is the speed of the space probe divided by the speed of sound. So, the speed of space probe is 15,000 kilometers per hour, and we'll convert that into meters per second by multiplying by 1 hour for every 3600 seconds and then times by 1,000 meters per kilometer and then divided by 42 meters per second. And this gives a Mach number of 99. And to figure out the angle between the space probes velocity and the shock wave will go sine θ is the speed of sound divided by the speed of the object and so θ is the inverse sine of that ratio. So, it's the inverse sine of 42 meters per second divided by the speed of the space probe converted to meters per second. That gives about 0.58 degrees. So, this angle right in here would be 0.58 degrees.
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