At some instant the velocity components of an electron moving between two charge

Question

At some instant the velocity components of an electron moving between two charged parallel plates are vx and vy. Suppose the electric field between the plates is E (it is uniform and points only in the y direction). What are (a) the magnitude of the acceleration of the electron and (b) the y-component of electron's velocity when its x coordinate has changed by a distance d? State your answers in terms of the given variables, using e for the fundamental charge and me for the mass of an electron.

Part A is a= (eE/ m sub e) I just need help with part B

Explanation / Answer

As you calculated, the y acceleration ay = eE/me.

Using kinematics, the y velocity after the distance d (call it vy_final) has to be vy + ayt = vy + eEt/me where vy is the initial y velocity. All we need is the time t.

But t = d/vx where vx is the initial x velocity, which doesn't change since there is no force in the x direction.

Therefore vy_final = vy + eEd/vxme

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