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$u_t = -\frac{R}{f} (\frac{d\langle T\rangle}{dy})ln(\frac{P_1}{P_2})$


$u_{200hPa}-u_{1000hPa}=\frac{R}{f}  (\frac{d\langle T\rangle}{dy})ln(\frac{200hPa}{1000hPa})$

$u_{200hPa}-0= \frac{300J/kg \times K}{10^{-4}s^{-1}}(-0.008K/km)ln\frac{200}{1000}$
$=300\times10^{4}\times(-0.008)\times(-ln5)(kg m^2s^{-2}/kgK) s (K/km)$$=300\times8\times\frac{10}{6}\times10^{-2}m/s$$=40m/s$