Solution to 1996 Problem 38

The definition of the total relativistic energy is
\begin{align*}E := \frac{m c^2}{\sqrt{1 - u^2/c^2}}\end{align*}
The definition of the relativistic momentum is
\begin{align*}\mathbf{p} := \frac{m \mathbf{u}}{\sqrt{1 - u^2/c^2}}\end{align*}
So, the magnitude of the relativistic momentum is
\begin{align*}p = \frac{m u}{\sqrt{1 - u^2/c^2}}\end{align*}
\begin{align*}p c^2/u = E \Rightarrow u = \frac{p c^2}{E} = \frac{5 c}{10} = \boxed{c/2} \end{align*}
Therefore, answer (D) is correct.

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