To solve this problem, we need to calculate the geostrophic wind speed at a given latitude using the pressure gradient and the density of air. The geostrophic wind speed is given by the geostrophic wind equation:

\(V_g = \frac{1}{f \cdot \rho} \cdot \frac{\Delta P}{\Delta x}\)

where:

• \(V_g\) is the geostrophic wind speed.
• \(f\) is the Coriolis parameter, which can be calculated as \(f = 2 \cdot \Omega \cdot \sin(\phi)\), where \(\Omega = 7.2921 \times 10^{-5} \thinspace \text{rad/s}\) is the angular velocity of the Earth, and \(\phi\) is the latitude in radians.
• \(\rho = 1.25 \thinspace \text{kg/m}^3\) is the density of air.
• \(\frac{\Delta P}{\Delta x} = 5.0 \thinspace \text{mb per 100 km}\) is the pressure gradient, which we convert to SI units: \(1 \thinspace \text{mb} = 100 \thinspace \text{Pa}\) and f at a latitude of 30°:

• Latitude in radians: \(\phi = 30^{\circ} \times \frac{\pi}{180} = \frac{\pi}{6} \thinspace \text{radians}\)
• Coriolis parameter: \(f = 2 \cdot 7.2921 \times 10^{-5} \cdot \sin(\frac{\pi}{6})\)
• \(f = 2 \cdot 7.2921 \times 10^{-5} \cdot 0.5\)
• \(f = 7.2921 \times 10^{-5} \thinspace \text{rad/s}\)
• \(\frac{\Delta P}{\Delta x} = 5.0 \thinspace \text{mb per 100 km} = 5.0 \times 100 \thinspace \text{Pa} / 10^5 \thinspace \text{m} = 0.05 \thinspace \text{Pa/m}\)
• \(V_g = \frac{1}{7.2921 \times 10^{-5} \cdot 1.25} \cdot 0.05\)
• \(V_g = \frac{0.05}{9.115125 \times 10^{-5}}\)
• \(V_g = 548.6 \thinspace \text{cm/s} = 5.486 \thinspace \text{m/s}\)