The energy stored in the membrane is 
Explanation:
The capacitance of a parallel-plate capacitor is given by

where
k is the dielectric constant of the material
is the vacuum permittivity
A is the area of the plates
d is the separation between the plates
For the membrane in this problem, we have
k = 4.6


Substituting, we find its capacitance:

Now we can find the energy stored: for a capacitor, it is given by

where
is the capacitance
is the potential difference
Substituting,

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Answer:
v = -v₀ / 2
Explanation:
For this exercise let's use kinematics relations.
Let's use the initial conditions to find the acceleration of the electron
v² = v₀² - 2a y
when the initial velocity is vo it reaches just the negative plate so v = 0
a = v₀² / 2y
now they tell us that the initial velocity is half
v’² = v₀’² - 2 a y’
v₀ ’= v₀ / 2
at the point where turn v = 0
0 = v₀² /4 - 2 a y '
v₀² /4 = 2 (v₀² / 2y) y’
y = 4 y'
y ’= y / 4
We can see that when the velocity is half, advance only ¼ of the distance between the plates, now let's calculate the velocity if it leaves this position with zero velocity.
v² = v₀² -2a y’
v² = 0 - 2 (v₀² / 2y) y / 4
v² = -v₀² / 4
v = -v₀ / 2
We can see that as the system has no friction, the arrival speed is the same as the exit speed, but with the opposite direction.
Answer
2) 1.5×10-2 m
Explanation
The potential difference is related to the electric field by:
(1)
where
is the potential difference
E is the electric field
d is the distance
We want to know the distance the detectors have to be placed in order to achieve an electric field of

when connected to a battery with potential difference

Solving the equation (1) for d, we find

Answer:
56km
Explanation:
168 ÷ 240 = 0.7
0.7 × 80 = 56km
240 is the amount of minutes in 4 hours.
We divided 168 by 240 to get the distance covered in 1 minute. Afterwards, we needed 80 minutes so we multiplied the answer by 80.