The work done by the potential difference gets stored as its kinetic energy.
∴12mv2=qV⇒v=(2qVm)1/2 (i)
When it enters the region xϵ[0,a), it experiences an electric field →E=E^j
Time taken to cross the region: vt=a
⇒t=av=a(m2qV)1/2 (ii)
The distance travelled in y-direction during this time is
y=12qEmt2=12×qEm×a2×m2qV
⇒y=14Ea2V
Hence, the particle meets the line x=a at point
(x,y)=(a,14Ea2V)