Answer
\[
2.14 \mathrm{mi} / \mathrm{s}
\]
Work Step by Step
Evaluate the integral for $b=400, a=0$, using the antiderivative
\[
\begin{array}{l}
v \approx\left[9-191,000 \int_{0}^{400} \frac{1}{(x+3963)^{2}} d x\right]^{1 / 2} \\
=\left[9-191,000\left(-\frac{-1}{3963}+\frac{-1}{400+3963}\right)\right]^{1 / 2} \\
=\left[9-191,000\left(2.31 \times 10^{-5}\right)\right]^{1 / 2} \\
=(4.5879)^{1 / 2} \approx 2.14 \mathrm{mi} / \mathrm{s}
\end{array}
\]
