What happens when the angle changes?

[judas_priest]

Hey,
I can't get through this problem from electrostatics.

Here's my attempt

$F=-eE$
It travels from point A $(a,0)$ to the point B, given by coordinates $(2a,d)$
For it to travel along that path, the electron needs to travel at an angle $tan(θ) = d/a$
(got the slope from the equation of line using the coordinates.)
Now, how does it change it's path to making 30 degrees with x-axis without being acted upon by a force.
I can't get anywhere from here.
Also, if electric field lines don't intersect, when it changes it's path to making 30 degrees, doesn't it intersect, because before reaching the point B, it was moving at an angle d/a

 

[voko]

What makes you think the electron travels along a straight line? Compare that with the gravity close to the Earth. It is also uniform and constant. Will anything with some initially horizontal velocity travel along a straight line close to the Earth?

 

[Doc Al]

For it to travel along that path, the electron needs to travel at an angle $tan(θ) = d/a$
(got the slope from the equation of line using the coordinates.)

Don't assume that the electron travels in a straight line.

Consider the x and y components of the velocity separately. Which direction must the field point?