How Does an Electric Field Affect Electron Trajectory in a Cathode Ray Tube?

[penzoate]

Homework Statement

An electron with the kinetic energy of 2.6e-6 Joules is moving to the right along the axis of a cathode ray tube. the length of the cathode ray tube is 16 cm and the length of the deflection inside the cathode ray tube is 4 cm. The electric field = 2e4*N/C. Everywhere else the electric field is zero.
a:) how far is the electron from the axis of the tube when it reaches the end of the plates?
my solution:
Energy =.5*m*v^2 give the initial velocity.

(2*(2e-16 Joules)/(9.11e-31 kg))^.5=v
to find time, I used kinematic equation
x=x(0)+vt --> x-x(0)/v=t --> 16 m/v=t x isthe total length of the cathode ray tube
a=E*q/m(electron)
y=.5*a*t^2

not surehow to find x-component for the velocity, y or time t. Any other variables in this problems I should consider?

Homework Equations

The Attempt at a Solution

 

[Mindscrape]

As I understand the problem the initial velocity is all in the x direction, and then the electric field applied a force to the charge in the y direction. If you know the length of the cathode ray tube, then you can figure out the time. If you know the time you can find how far up it went, how far off the axis it is.