Projectile Motion Q: Solve Force & Trajectory of Electron in Electric Field

[magicuniverse]

1. Homework Statement

When the terminals of a 100V battery are connected to two large parallel horizontal plates 1 cm apart the electric field E between them has a magnitude of E=10^4 NC^-1, and is directed upward. Compute the force on the electron in the field and compare it with the weight of the electron.

[charge on an electron = -1.6x10^-19, mass of electron =9.11x10^-31kg]

If the electron were projected into the field with an initial horizontal velocity V0, find the equation of its trajectory of the form y=f(x) (take y vertical and x horizontal).


3. The Attempt at a Solution

I have a solution to the first part using the formula: F=qE, I found f = -1.6x10^-15.
I then wored out the weight using w=mg, getting 8.94x10^-30 N. I compared this and explained that as F is vastly bigger than W the object will move upwards rather than downwards towards gravity.

However I have no clue on how to do the second part, please help.

 

[Astronuc]

Well the electric field points up, and it points from + to - charges, so the electron would accelerate downward since it has a negative charge and would be attracted to the + charges.

Now for determined y = y(x), we have a parametric equation.

What is x(t) for a constant velocity of V0?

Now what is y(t) for a particle under constant acceleration in y (in the negative y direction)?

Find y(t) = f(t) then substitute in t = f(x) from x(t) equation.