Randall D. Knight — Dynamics II: Motion in a Plane: Problem 34

A charged particle in an electric field experiences an electric force \(\vec{F}_E = q\vec{E}\), where \(q\) is the charge in coulombs (C) and \(\vec{E}\) is the electric field in N/C. This is analogous to the gravitational force \(m\vec{g}\) on mass \(m\). A small 5.0 mg particle charged to \(3.0 \times 10^{-10} \text{ C}\) is fired horizontally at \(\vec{v}_0 = 0.75\hat{i} \text{ m/s}\) into a horizontal electric field \(\vec{E} = 1.0 \times 10^5\hat{i} \text{ N/C}\) from a height of 15 cm. How far has the particle traveled horizontally when it hits the ground? Assume that the motion takes place in a vacuum. Be careful converting mg to the appropriate SI units!