Answer:
a) ΔV = 25.59 V, b) ΔV = 25.59 V, c) v = 7 10⁴ m / s, v/c= 2.33 10⁻⁴ ,
v/c% = 2.33 10⁻²
Explanation:
a) The speed they ask for electrons is much lower than the speed of light, so we don't need relativistic corrections, let's use the concepts of energy
starting point. Where the electrons come out
Em₀ = U = e DV
final point. Where they hit the target
Em_f = K = ½ m v2
energy is conserved
Em₀ = Em_f
e ΔV = ½ m v²
ΔV =
mv²/e (1)
If the speed of light is c and this is 100% then 1% is
v = 1% c = c / 100
v = 3 10⁸/100 = 3 10⁶6 m/ s
let's calculate
ΔV =
ΔV = 25.59 V
b) Ask for the potential difference for protons with the same kinetic energy as electrons
K_p = ½ m v_e²
K_p =
9.1 10⁻³¹ (3 10⁶)²
K_p = 40.95 10⁻¹⁹ J
we substitute in equation 1
ΔV = Kp / M
ΔV = 40.95 10⁻¹⁹ / 1.6 10⁻¹⁹
ΔV = 25.59 V
notice that these protons go much slower than electrons because their mass is greater
c) The speed of the protons is
e ΔV = ½ M v²
v² = 2 e ΔV / M
v² =
v² = 49,035 10⁸
v = 7 10⁴ m / s
Relation
v/c = 
v/c= 2.33 10⁻⁴
The charges have opposite sign and magnitude 
Explanation:
The magnitude of the electrostatic force between two electric charges is given by Coulomb's law:
where:
is the Coulomb's constant
are the two charges
r is the separation between the two charges
In this problem, we have:
F = 3.60 N is the force between the two charges
r = 30 cm = 0.30 m is their separation
The two charges have same magnitude, so

So we can rewrite the equation as

And solving for q:

Moreover, the force between the charges is attractive: we know that charges of same sign repel each other while charges of opposite sign attract each other, therefore the charges in this problem have opposite sign, so

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the answer is heat engine
The magnitude of their resultant vector is 4.6 meters/seconds
Since we are to add the velocity vectors in order to find the magnitude of their resultant vector.
Hence:
Resultant vector magnitude=5.8 meters/seconds + (1.2 meters/seconds)
Resultant vector magnitude=5.8 meters/seconds-1.2 meters/seconds
Resultant vector magnitude 4.6 meters/seconds
Inconclusion The magnitude of their resultant vector is 4.6 meters/seconds
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