Motion of Charged Particles in Electric Fields

[CARL0001]

Homework Statement

This is the question: An electron at rest of mass 9.11 × 10−31 kg is accelerated through a potential difference of 350 V. It then enters some deflecting plates of 50 V with dimensions as shown. Calculate the distance x (deflection of the electron) (Charge on an electron is 1.6 × 10−19 C)

Given Diagram: https://gyazo.com/73ada230623b2ba00a80f5be8001fade

Homework Equations

W = FEΔd = ½mv2 = qΔV , Δt = Δd / v

https://gyazo.com/0b2211e627a646ec5437e72c0848e6d9

The Attempt at a Solution

So the question is asking to find the displacement in the y direction which is x on the diagram. i first found the original velocity between the vertical plates. in order to get the original velocity i used the following equation qΔV= ½mv2. i rearranged the formula and solved for v which i got to be 1.1 x 10^7 m/s. from my understanding this is the initial velocity of the electron when it enters the horizontal plates. I'm confused where to go from here. i can't find any practice examples similar to this type of question. I'm confused whether or not you need to split this section into vertical and horizontal components. i think next i have to find the electric force and then use that to find the acceleration. then i think you can use
Δt = Δd / v to find the time between the plates. after this i think you can find the displacement using one of the 5 kinematic equations. however I'm confused since i don't know if you need to split this up into different components.

 

[Dadface]

Have you covered projectile (parabolic motion) in uniform gravitational fields? If so you can use similar techniques to solve your problem.
HINT In one direction the electron continues moving with constant velocity and perpendicular to that it moves with constant acceleration.

 

[CARL0001]

Have you covered projectile (parabolic motion) in uniform gravitational fields? If so you can use similar techniques to solve your problem.
HINT In one direction the electron continues moving with constant velocity and perpendicular to that it moves with constant acceleration.

No I'm not familiar with this method, however is my method correct?

 

[haruspex]

Δt = Δd / v

No, that is only valid for constant velocity. Here you have constant acceleration in the direction of the field. That makes it just like projectiles in near-Earth gravity.
Look up SUVAT.