$A+8\mathrm{.}00C$ enters midway into the electric field $(100\frac{N}{C})$ created by two oppositely charged horizontal plates $($positive on top$)$ placed $24\mathrm{.}0$ cm apart. If the charge $(m=25\mathrm{.}0mg)$ enters with a horizontal velocity of $15\mathrm{.}0\frac{m}{s}$ right, find:

a$)$ The vertical velocity of the charge $0\mathrm{.}100$ s after it enters the electric field. $(3$ marks$)$

b$)$ The horizontal distance that the charge travels before it strikes the negative plate.$(3$ marks$)$