Answer:
The Mach number of the jet is approximately 1.025, meaning it is flying at a speed 1.025 times the speed of sound in the given air temperature. This indicates that the jet is flying slightly faster than the speed of sound and is considered supersonic.
Step-by-step explanation:
To calculate the Mach number of the jet, we first need to find the speed of sound in the given air temperature. The speed of sound in air can be calculated using the formula:
a = √(γ * R * T)
where:
- a is the speed of sound in m/s
- γ is the adiabatic index (ratio of specific heat capacities), which is approximately 1.4 for air
- R is the specific gas constant for air, approximately 287 J/(kg·K)
- T is the temperature in Kelvin (K)
First, convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25.0 + 273.15 = 298.15 K
Now, calculate the speed of sound:
a = √(1.4 * 287 * 298.15)
a ≈ 347.42 m/s
Next, we need to convert the jet's speed from km/h to m/s:
v(m/s) = v(km/h) * (1000 m/km) / (3600 s/h)
v(m/s) = 1281.6 * 1000 / 3600 ≈ 356.00 m/s
Finally, we can calculate the Mach number (M) using the formula:
M = v / a
M = 356.00 / 347.42 ≈ 1.025
The Mach number of the jet is approximately 1.025.
The Mach number is a dimensionless quantity that represents the ratio of an object's speed (in this case, the jet) to the speed of sound in the surrounding medium (air). A Mach number of 1.025 means that the jet is flying at a speed that is 1.025 times the speed of sound in the air at the given temperature. In this case, the jet is flying slightly faster than the speed of sound and is considered to be supersonic.