Answer
$L'=1.13m$
Work Step by Step
The contracted length of an object is equal to $$L'=\frac{L}{\gamma}$$ Gamma is equal to $$\gamma=\frac{1}{\sqrt{1-\beta^2}}$$ where $\beta=\frac{v}{c}$. Solving for $\beta$ yields $$\beta=\frac{20.0mi/h}{25.0mi/h}=0.800$$ Substituting the known value of $\beta=0.800$ yields a gamma value of $$\gamma=\frac{1}{\sqrt{1-0.800^2}}=1.67$$ Substituting known values of $\gamma=1.67$ and $L=1.89m$ yields a contracted length of $$L'=\frac{1.89m}{1.67}=1.13m$$
