Kinematics with Electrostatics!

A particle with mass $3 \text{ kg}$ and charge $+2 \text{ C}$ is launched with initial speed $2 \text{ m/s}$ from the top of a tower at height $\displaystyle H=5m$ . The particle velocity initially makes a variable angle of $\theta^\circ$ with the horizontal plane at the height such that $0\leq\theta\leq90$ .

There is a uniform ambient electric field with strength $6 \text{ N/C}$ , which points upwards with an angle of $60^\circ$ with respect to the horizontal plane at height $\displaystyle H$ . There is an ambient gravitational field of $10\text{ m/s}^2$ in the downward, vertical direction.

If $\displaystyle R_{max}$ represents the maximum possible Range of the particle (in meters), then evaluate $\displaystyle R_{max}$ .

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