Answer:
See the answers below
Explanation:
We can solve this problem using the principle of energy conservation. That is, the energy is conserved before and after dropping the bag.
For this case we have mechanical energy, which is the sum of the kinetic and potential energies.

where:

Ek = kinetic energy [J] (units of Joules)
Ep = potential energy [J]
In the final Energy (2), there is only potential energy. since when the balloon reaches the maximum height its velocity is zero, that is, there is no kinetic energy.
A)
![m*g*h+\frac{1}{2}*m*v^{2} =m*g*h_{1} \\9.81*50+0.5*(15)^{2}=9.81*h_{1}\\h_{1} = 61.46 [m]](https://tex.z-dn.net/?f=m%2Ag%2Ah%2B%5Cfrac%7B1%7D%7B2%7D%2Am%2Av%5E%7B2%7D%20%3Dm%2Ag%2Ah_%7B1%7D%20%5C%5C9.81%2A50%2B0.5%2A%2815%29%5E%7B2%7D%3D9.81%2Ah_%7B1%7D%5C%5Ch_%7B1%7D%20%3D%2061.46%20%5Bm%5D)
B)
With the value calculated above we can find the acceleration of the balloon.
The distance traveled is the difference between the maximum height and 50 meters.
![x = 61.46-50\\x = 11.46[m]](https://tex.z-dn.net/?f=x%20%3D%2061.46-50%5C%5Cx%20%3D%2011.46%5Bm%5D)
With the following equation of kinematics.

![0 = 15^{2} +2*a*11.46\\a = - 9.816 [m/s^{2} ]](https://tex.z-dn.net/?f=0%20%3D%2015%5E%7B2%7D%20%2B2%2Aa%2A11.46%5C%5Ca%20%3D%20-%209.816%20%5Bm%2Fs%5E%7B2%7D%20%5D)
The negative sign indicates that the acceleration acts downward. That is, in the opposite direction to the movement.
We can use the following equation of kinematics to find the final velocity after 4 seconds.
![v_{f}=v_{o}-a*t\\v_{f}=15-9.816*(4)\\v_{f}=-24.24 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D-a%2At%5C%5Cv_%7Bf%7D%3D15-9.816%2A%284%29%5C%5Cv_%7Bf%7D%3D-24.24%20%5Bm%2Fs%5D)
Now the distance:
![v_{f}^{2} =v_{o}^{2}-2*a*x\\(24.24)^{2} =(15)^{2} -2*9.81*x\\x = 18.48 [m]\\x_{f}=50+18.48 = 68.48 [m]](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%20%3Dv_%7Bo%7D%5E%7B2%7D-2%2Aa%2Ax%5C%5C%2824.24%29%5E%7B2%7D%20%3D%2815%29%5E%7B2%7D%20-2%2A9.81%2Ax%5C%5Cx%20%3D%2018.48%20%5Bm%5D%5C%5Cx_%7Bf%7D%3D50%2B18.48%20%3D%2068.48%20%5Bm%5D)
c) Using the following equation of kinematics.
![v_{f}=v_{o}-a*t\\0 = 15-9.81*t\\15=9.81*t\\t = 1.52 [s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D-a%2At%5C%5C0%20%3D%2015-9.81%2At%5C%5C15%3D9.81%2At%5C%5Ct%20%3D%201.52%20%5Bs%5D)
Answer:
T = 1.12 10⁻⁷ s
Explanation:
This exercise must be solved in parts. Let's start looking for the electric field in the axis of the ring.
All the charge dq is at a distance r
dE = k dq / r²
Due to the symmetry of the ring, the field perpendicular to the axis is canceled, leaving only the field in the direction of the axis, if we use trigonometry
cos θ =
dEₓ = dE cos θ
cos θ = x / r
substituting
dEₓ =
DEₓ = k dq x / r³
let's use the Pythagorean theorem to find the distance r
r² = x² + a²
where a is the radius of the ring
we substitute
dEₓ =
we integrate
∫ dEₓ =k \frac{x}{(x^2 + a^2 ) ^{3/2} } ∫ dq
Eₓ = 
In the exercise indicate that the electron is very central to the center of the ring
x << a
Eₓ =
if we expand in a series
we keep the first term if x<<a
Eₓ =
the force is
F = q E
F = 
this is a restoring force proportional to the displacement so the movement is simple harmonic,
F = m a
the solution is of type
x = A cos (wt + Ф)
with angular velocity
w² =
angular velocity and period are related
w = 2π/ T
we substitute
4π² / T² = \frac{keQ}{m a^3}
T = 2π
let's calculate
T = 2π
T = 2π pi 
T = 2π 17.9 10⁻⁹ s
T = 1.12 10⁻⁷ s
Law of conservation is what ur referring to
<u>Answer:</u>
The acceleration due to gravity on that planet = 72.76 
<u>Explanation:</u>
Weight of person in earth = 717 N
We know that weight = mg
Acceleration due to gravity of earth = 
So mass of person = 717/9.8 = 73.16 kg
Mass of body is constant everywhere, so mass of person on the surface of a nearby planet = 73.16 kg
Weight on the surface of a nearby planet = 5320 N = mg', where g' is the acceleration due to gravity value of the nearby planet.
So 5320 = 73.16*g'
g' = 72.76 
The acceleration due to gravity on that planet = 72.76 