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Answer :
Final answer:
The cruise speed of a Boeing 777-200LR, flying at an altitude of 35,000 feet at Mach 0.84, is approximately 247.8 m/s, calculated by multiplying the Mach number by the speed of sound at that altitude.
Explanation:
The subject of this question involves the application of physics concepts, particularly those related to fluid dynamics and aerodynamics. Specifically, the student is asked to calculate the cruise speed of a Boeing 777-200LR, given certain parameters about the aircraft.
To compute the cruise speed, we need to consider the cruising Mach number stated in the problem, Mach 0.84. The Mach number corresponds to the ratio of the aircraft's speed to the speed of sound in the surrounding medium, which varies with temperature according to the standard atmospheric temperature data. At 35,000 feet, this temperature is approximately -56.5°C, or 216.65K.
Given that the speed of sound in air is calculated using the formula v = sqrt(gamma * R * T) where gamma is the ratio of specific heats (1.4 for air), R is the specific gas constant for air (287 J/(Kg*K)), and T is the temperature in Kelvin, we can calculate the speed of sound at this altitude.
Substituting these values in, we get a speed of sound of approximately 295 m/s. To find the cruise speed of the airplane, we multiply this by the Mach number: v = Mach * Speed of sound = 0.84 * 295 m/s = 247.8 m/s. Therefore, the cruise speed of the Boeing 777-200LR is 247.8 m/s.
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Final answer:
The cruise speed of a Boeing 777-200LR at an altitude of 35,000 ft and at Mach 0.84 is approximately 248 m/s.
Explanation:
The cruise speed of a Boeing 777-200LR cruising at Mach 0.84 at an altitude of 35,000 ft can be calculated using the speed of sound at that altitude.
The speed of sound at 35,000 ft is approximately 295 m/s.
So, the cruise speed is Mach 0.84 times the speed of sound (295 m/s) which gives approximately 248 m/s.
The Mach number is a dimensionless quantity representing the ratio of the speed of an object moving through air to the local speed of sound.
Therefore, in this case, the design speed of the Boeing 777-200LR at the cruising altitude is Mach 0.84, which corresponds to the actual speed of 248 m/s.
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