A steel sphere is released so that it falls vertically onto a horizontal metal plate. It strikes the plate with speed $u$, then departs from it with speed $v$, and rises vertically again to half of its starting height. Which expression represents $\frac{v}{u}$?
- A$\frac{1}{2^2}$
- B$\frac{1}{2}$
- C$\frac{1}{\sqrt{2}}$
- D$1 - \frac{1}{\sqrt{2}}$