AP Physics C — Projectile Motion Under Uniform Electric Field

The image above depicts a proton of mass and charge being launched with a velocity into an Electric Field being created by two charged plates with length and distance apart .

Question

Create an equation for the trajectory of the particle.

The only force on the object is the electric force, so we can write:

We can use kinematic equations to find acceleration. In the direction:

In the direction:

Putting the two together: