What is the impact speed of the proton in a 4850V capacitor?

[prokaryote]

Homework Statement

A parallel-plate capacitor is charged to 4850 V. A proton is fired into the center of the capacitor at a speed of v0=2.81 * 10^5 m/s. The proton is deflected while inside the capacitor, and the plates are long enough that the proton will hit one of them before emerging from the far side of the capacitor. What is the impact speed of the proton?

V = 4850 V
Vi = 2.81 * 10^5 m/s
charge of proton = 1.602*10^-19 C
mass of proton = 1.7*10^-27 kg

Homework Equations

Ki + Ui = Kf + Uf

The Attempt at a Solution

https://imgur.com/a/MIsUX
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I've checked my answer several times on both a mathematical and conceptual level, and I have no idea what I'm doing wrong. Thanks for taking the time to read this.

 

[TSny]

Hello.

"Fired into the center" implies something about the potential difference between the starting point and the point where the proton hits the plate.

 

[prokaryote]

Hello.

"Fired into the center" implies something about the potential difference between the starting point and the point where the proton hits the plate.

Got it. I was going off of the erroneous assumption that the voltage is uniform throughout the capacitor. I halved the voltage (as it is in the center) and got the right answer. Thank you so much!

 

[TSny]

OK. Good.