In a free atmosphere without friction, if the pressure increases by one kilo Pascal eastward across a distance of $200$ $\mathrm{km}$, the magnitude of geostrophic flow (in $m s^{-1}$ ) is $\_\_\_\_$. (rounded off to two decimal places)
[Density of air is $1.029 \mathrm{~kg} \mathrm{~m}^{-3}$ and the Coriolis parameter is $10^{-4} \mathrm{~s}^{-1}$.]
