Question

An object is moving with a Mach number of 0.6 in an ideal gas environment, which is at a temperature of 350 K. The gas constant is 320 J/kg.K and ratio of specific heats is 1.3. The speed of object is \(\underline{\hspace{1cm}}\) m/s (round off to the nearest integer).

Hint:

The speed of an object moving at a given Mach number can be calculated by multiplying the Mach number by the speed of sound in the medium.

Answer 1

Correct Answer: 228 - 230

The Mach number \(M\) is given by: \[ M = \frac{V}{c}, \] where:
- \(M = 0.6\) is the Mach number,
- \(V\) is the speed of the object,
- \(c\) is the speed of sound in the gas, which can be calculated as:
\[ c = \sqrt{k \cdot R \cdot T}, \] where: - \(k = 1.3\) is the ratio of specific heats, - \(R = 320 \, \text{J/kg.K}\) is the gas constant, - \(T = 350 \, \text{K}\) is the temperature. Substituting the values: \[ c = \sqrt{1.3 \cdot 320 \cdot 350} \approx \sqrt{146240} \approx 382.5 \, \text{m/s}. \] Now, using the Mach number to find the speed: \[ V = M \cdot c = 0.6 \times 382.5 \approx 229.5 \, \text{m/s}. \] Thus, the speed of the object is: \[ \boxed{228 \, \text{to} \, 230 \, \text{m/s}}. \]