Find the max speed so that an electron doesn't hit the plate

[Whiteclaws]

Homework Statement

An electron is fired from x = 0 with an unknown V0 at 45 degs to the horizontal between two parallel plates separated by 2 cm. Electric field is 103 j N/C. Find:

a) The max value of V0 so that the electrons don’t hit the upper plate
3.75 * 106 m/s

Homework Equations

If you find acceleration, it is essentially a kinetics problem
Eq = ma

The Attempt at a Solution

a = -1.76 * 10^14 j m/s^2
0.02 = v0t -8.8 * 10^13 t^2
Then I have no idea how to solve for either t or V0,
For anybody who has the book university physics, it's number 33

 

[cnh1995]

0.02 = v0t -8.8 * 10^13 t^2

Is the initial velocity in the upward direction V_o? What do you know from the given 45° angle?

Then I have no idea how to solve for either t or V0,

You need one more equation if you want to involve time.
Instead, you can solve it with only one equation.
If initial vertical velocity is at its maximum (so that the electron doesn't "hit" the upper plate), what should be the final velocity?

 

[Whiteclaws]

Is the initial velocity in the upward direction V_o? What do you know from the given 45° angle?

You need one more equation if you want to involve time.
Instead, you can solve it with only one equation.
If initial vertical velocity is at its maximum (so that the electron doesn't "hit" the upper plate), what should be the final velocity?

V0 is a vector but for simplicity's sake let's assume that it's Vy initial
I'll convert it later

 

[Whiteclaws]

I SEE, IF V0 IS MAXIMIZED, THAT MEANS THAT VY AT THE TOP IS 0, SINCE IT'S AN ARC! SO
V^2 = v0^2 + 2adelta y
0 = (Vosin45)^2 + 2a delta y
and you SOLVE FOR VO!
thanks for the HINT!