Mastering Physics: Electron turning 90 degrees in capacitor

[danielhep]

Homework Statement

A problem of practical interest is to make a beam of electrons turn a 90∘ corner. This can be done with the parallel-plate capacitor shown in the figure (Figure 1) . An electron with kinetic energy 2.0×10−17 J enters through a small hole in the bottom plate of the capacitor.
What strength electric field is needed if the electron is to emerge from an exit hole 1.0 cm away from the entrance hole, traveling at right angles to its original direction?

Homework Equations

V_f²=V_i²+2ad
F=ma
F=Eq
K (kinetic energy) = 1/2mv²

The Attempt at a Solution

The electric field needs bring vertical velocity to zero and horizontal velocity to what the vertical velocity was. I should just be able to find what E-field is necessary to bring the vertical velocity to zero without having to worry about the horizontal velocity, I think.

V_i=(2K/m)^1/2
d=.01*cos45
0=(2K/m)+2a*.01*cos45
-K/(m(.01*cos45))=a

Now finding acceleration in terms of E
qE=ma
qE/m=a

Combining them:
-K/(m(.01*cos45))=qE/m
-K/(q(.01*cos45))=E

Now, when I go through this I get 17655 N/C, which seems close (right order of magnitude), but according to Mastering it's not correct. Any help would be appreciated, thank you!

 

[TSny]

V_i=(2K/m)^1/2
d=.01*cos45
0=(2K/m)+.01*cos45

Did you leave out the acceleration in the second equation above?
[EDIT: Should there also be a factor of 2 in the second term?]

-K/(m(.01*cos45))=a

What happened to the factor of 2? [EDIT: I think this is ok. See edited comment above]
Is the acceleration "a" the magnitude of the total acceleration, or does it represent just a component of the acceleration?

 

[danielhep]

Did you leave out the acceleration in the second equation above?
[EDIT: Should there also be a factor of 2 in the second term?

What happened to the factor of 2? [EDIT: I think this is ok. See edited comment above]
Is the acceleration "a" the magnitude of the total acceleration, or does it represent just a component of the acceleration?

Fixed the original post, thanks.

a represents the y component of the acceleration... Which means I'm just finding the y component of the electric field...

I just took my answer and used the pythagorean theorem to find the total magnitude and it was correct! Thank you! That was a perfect hint.

 

[TSny]

Good work!