A proton moves at $4\mathrm{.}60{10}^5\frac{m}{s}$ in the horizontal direction. It enters a uniform vertical electric field with a magnitude of $8\mathrm{.}20{10}^3\frac{N}{C}.$ Ignore anly gravitational effects.

$($a$)$ Find the time interval required for the proton to travel $4\mathrm{.}50cm$ horizontally. ns

$($b$)$ Find its vertical displacement during the time interval in which it travels $4\mathrm{.}50cm$ horizontally. $($Indicate direction with the sign of your answer.$)nm$

$($c$)$ Find the horizontal and vertical components of its velocity after it has traveled $4\mathrm{.}50cm$ horizontally.

vec$(v)=,i+i$