At an altitude of 24,000 feet a Pitot tube measures a total pressure of 0.5564 bar. Determine the equivalent airspeed (in metres per second) of the aircraft (assuming ISA conditions).

To determine the equivalent airspeed of an aircraft using the total pressure measured by a Pitot tube, we need to find the air density at the altitude of 24,000 feet, convert that to appropriate units, and then calculate the equivalent airspeed.

**Step 1: Understanding the Problem**

The total pressure \( P_t \) measured by the Pitot tube is given as 0.5564 bar. We need to convert this pressure to Pascals for calculations, since:
\[
1 \text{ bar} = 100,000 \text{ Pa}
\]

Thus:
\[
P_t = 0.5564 \text{ bar} = 0.5564 \times 10^5 \text{ Pa} = 55,640 \text{ Pa}
\]

**Step 2: Calculate Static Pressure at 24,000 feet**

At an altitude of 24,000 feet (approximately 7,315 meters), we can use the International Standard Atmosphere (ISA) model to find the static pressure \( P_s \).

Using the ISA, at 24,000 feet, the temperature \( T \approx -6.5 \text{ °C} = 266.65 \text{ K} \), and the standard pressure at this altitude \( P_s \approx 0.2924 \text{ bar} \) or \( 29,240 \text{ Pa} \).

**Step 3: Calculate Air Density**

The air density \( \rho \) can be found using the ideal gas law:
\[
\rho = \frac{P_s}{R T}
\]
where:
- \( R \) (specific gas constant for dry air) \( \approx 287.05 \, \text{J/(kg} \cdot \text{K)} \)
- \( P_s = 29,240 \text{ Pa} \)
- \( T = 266.65 \text{ K} \)

Substituting the values:
\[
\rho = \frac{29,240}{287.05 \times 266.65} \approx \frac{29,240}{7650.2} \approx 3.82 \, \text{kg/m}^3
\]

**Step 4: Determine Equivalent Airspeed (EAS)**

The dynamic pressure \( q \) is given by:
\[
q = P_t - P_s = 55,640 \text{ Pa} - 29,240 \text{ Pa} = 26,400 \text{ Pa}
\]

The equivalent airspeed (EAS) can be calculated using the formula:
\[
EAS = \sqrt{\frac{2q}{\rho}}
\]
Substituting the values:
\[
EAS = \sqrt{\frac{2 \times 26,400}{3.82}} = \sqrt{\frac{52,800}{3.82}} \approx \sqrt{13,831.64} \approx 117.03 \text{ m/s}
\]

**Conclusion**

The equivalent airspeed of the aircraft at the altitude of 24,000 feet with the given conditions is approximately:
\[
\boxed{117.03 \, \text{m/s}}
\]