In a certain region surrounding the origin of the coordinate, `vec(B) = 5 xx 10^(-4) hat(k) T` and `vec(E ) = 5 hat(k)` V/m. A proton enters the fields at the origin with an intial velocity `vec(V_(0)) = 2.5 xx 10^(5) hat(i)` m/s. Discribe the protons motion and give its position after three complete revolutions

Explanation

To solve the problem, we need to analyze the motion of a proton in the presence of both electric and magnetic fields. The proton experiences forces due to these fields, which will affect its trajectory. Let's break down the solution step by step.

### Step 1: Identify the Forces Acting on the Proton
The proton is subjected to two forces:
1. **Electric Force (\( \vec{F_E} \))**: This force is given by \( \vec{F_E} = q \vec{E} \), where \( q \) is the charge of the proton and \( \vec{E} \) is the electric field.
2. **Magnetic Force (\( \vec{F_B} \))**: This force is given by \( \vec{F_B} = q \vec{V} \times \vec{B} \), where \( \vec{V} \) is the velocity of the proton and \( \vec{B} \) is the magnetic field.

### Step 2: Calculate the Electric Force
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