Answer:
Please see below as the answer is self-explanatory
Explanation:
Assuming that the electric field is pointing upward this will produce a downward force on the electron. Neglecting the effect of gravity, according to Newton's 2nd Law, the force on the electron due to the field, produces an acceleration, that can be found solving the following equation:
F = me*a = qe*E ⇒ a = qe*E / me
If the electric field is uniform, the acceleration that produces is constant, so, we can use the kinematic equation that relates displacement and acceleration with time:
x = v₀*t + 1/2*a*t² = v₀*t +1/2*(qe*E/me)*t²
Now, for a proton falling, if the direction of the field is reversed (pointing downward) it will accelerate the proton downward.
Using the same reasoning as above, we get the value of the acceleration as follows:
F = mp*a = qp*E ⇒ a = qp*E / mp
The equation for displacement is just the following:
x = v₀*t + 1/2*a*t² = v₀*t +1/2*(qp*E/mp)*t²
We know that qe = qp = 1.6*10⁻¹⁹ coul, but mp = 1,836 me, so, for the same displacement, the time must be much less for the electron, that has an acceleration 1,836 times higher.
When both objects fall freely the same distance under the sole influence of gravity, if the initial velocity is the same, the time must be the same also, as the fall time doesn't depend on the mass of the object.
