Bounce!

A uniform electric field $\vec{E}$ exists at an angle $\theta$ with respect to the ground. A particle of mass $m$ and charge $q$ is projected from the ground along the direction of the electric field with an initial velocity $\vec{v}$ .

If the coefficient of restitution between the particle and the ground is $e$ , find the distance travelled by the particle between the first and second impacts with the ground.

Details & Assumptions:

1. $|\vec{E}| = 15 NC^{-1}$
2. $\theta = 30^{\circ}$
3. $m = 3 kg$
4. $q = 2 C$
5. $|\vec{v}| = 20 ms^{-1}$
6. $e = 0.5$

Assume the gravitational field is uniform. Take $g = 10 ms^{-2}$ .