Charge released from rest near a grounded conductor

[radonballoon]

Homework Statement

A charge q of mass m is released a distance d from a semi-infinite grounded conductor. How long will it take the charge to reach the conductor?

So I tried this using the method of images, and I can easily find the force on the charge a distance d away:

F = -q^2 zhat / (4 pi epsilon0 (2d)^2)

But I'm not sure where to go from here.

Any help would be fantastic

 

[BerryBoy]

$$F= - \frac{q^2}{4 \pi \epsilon_0 (2d)^2}\hat{z}$$
$$F = m \frac{\partial^2 r}{\partial t^2}$$

Does this help??

Sam =]

 

[radonballoon]

Not really, I'm aware of the definition of Force. If you'd like to show how to integrate that I'd be grateful, but I have no idea.

 

[borgwal]

d is a constant here: instead, write the force as a function of the variable z (the variable distance to the conductor). Then, as an intermediate step, can you get an equation for the velocity dz/dt of the charge as a function of z?

 

[radonballoon]

Thanks that was what I needed to do.

Just as a followup:
change second derivative of z to dv/dz*dz/dt=dv/dz*v
from there it's pretty easy