a b c d

c

If it fails to stop the metal plate then its velocity just before reaching the metal plate become zero. From work energy theorem work done = change in kinetic energy $ -eEx = 0 - \frac{1}{2}mv^2$ $\Rightarrow x = \frac{mv^2}{2eE} = \frac{mv^2}{2e\frac{\sigma}{\epsilon_0}}=0.44 mm$