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 ____________m/s (round off to the nearest integer)

The correct answer is 229 (rounded to the nearest integer, or 228.94 as the exact decimal value).

To find the speed of the object, we can follow a step-by-step approach based on the properties of the ideal gas and the definition of the Mach number.

Step 1: Identify the given values from the problem statement:
- Mach number, $M=0.6$
- Temperature of the ideal gas, $T=350\text{K}$
- Gas constant, $R=320\text{J/kg}\cdot \text{K}$
- Ratio of specific heats, $\gamma =1.3$

Step 2: Calculate the speed of sound in the gas:
The speed of sound ($C$) in an ideal gas is given by the formula:
$$C=\sqrt{\gamma RT}$$ Substituting the given values into the formula:
$$C=\sqrt{1.3\times 320\times 350}$$ $$C=\sqrt{145600}\approx 381.575\text{m/s}$$

Step 3: Calculate the speed of the object:
The Mach number ($M$) is defined as the ratio of the object's speed ($V$) to the speed of sound ($C$) in the medium:
$$M=\frac{V}{C}$$ Rearranging the equation to solve for the speed of the object ($V$):
$$V=M\times C$$ Substituting the values we have:
$$V=0.6\times 381.575=228.945\text{m/s}$$

Rounding off to the nearest integer, we get:
$$V\approx 229\text{m/s}$$