A steel sphere is let go so that it falls straight down onto a level metal plate. It strikes the plate with speed $u$, rebounds from it with speed $v$, and rises vertically to half its initial height. Air resistance is to be ignored. Which expression gives the value of $\frac{v}{u}$?
- A$\frac{1}{2^2}$
- B$\frac{1}{2}$
- C$\frac{1}{\sqrt{2}}$
- D$1 - \frac{1}{\sqrt{2}}$