$[-/8$ Points$]$

SERPSE$1022\mathrm{.}6.$P$\mathrm{.}026.$

Protons are projected with an initial speed $v_1=9\mathrm{.}67k\frac{m}{s}$ from a field$-$free region through a plane and into a region where a uniform electric field vec$(E)=-720$hat$(j)\frac{N}{C}$ is present above the plane as shown in in the figure below. The initial velocity vector of the protons makes an angle $$ with the plane. The protons are to hit a target that lies at a horizontal distance of $R=1\mathrm{.}14mm$ from the point where the protons cross the plane and enter the electric field. We wish to find the angle $$ at which the protons must pass through the plane to strike the target.

$($a$)$ What analysis model describes the horizontal motion of the protons above the plane?

particle under constant velocity

particle under constant acceleration

particle in uniform circular motion

particle in simple harmonic motion

$($b$)$ What analysis model describes the vertical motion of the protons above the plane?

particle under constant velocity

particle under constant acceleration

particle in uniform circular motion

particle in simple harmonic motion

$($c$)$ Argue that $R=\frac{v_i^{2}sin(2{}_i)}{a}$ would be applicable to the protons in this situation.

This answer has not been graded yet.

$($d$)$ Use $R=\frac{v_j^{2}sin(2{}_j)}{g}$ to write an expression for $R$ in terms of $v_j,E,$ the charge and mass of the proton, and the angle $.($Use the following as necessary: $v_k,E,E_1{}_k,$ and $m_p$ for the mass of proton.$)$

$R=$

Part D only please