The conservation of mechanical energy allows to find the results for the velocity of the body when it is under the balcony and has a loss of energy due to friction are:
Mechanical energy is defined as the sum of kinetic energy plus potential energies. One of the main principles of physics is that energy cannot be created or destroyed unless it is transformed.
A reference system is a coordinate system with respect to which measurements are made, indicating that the height of the body is y₁= 1.89m above the balcony and the end point is y₂ = 2.20 m below the balcony. Let's set a reference frame with zero at the lowest point of the movement, therefore the highest point has a height.
h = y₁ + y₂
h = 1.89 + 2.20
h = 4.09 m
Let's find the initial energy at the highest point where the velocity is zero.
Em₀ = U = m g h
They indicate that it loses 10% of energy due to air resistance, the final energy is
[tex]Em_f = Em_o - \frac{Emo}{10}[/tex]
[tex]Em_f = 0.90 Em_o[/tex]
Let's write the final mechanical energy for the lowest point, at this point the height is zero.
[tex]Em_f[/tex] = K = ½ m v²
we substitute
½ m v² = 0.90 m g h
v = [tex]\sqrt{0.90 \ 2 \ g \ h }[/tex]
Let's calculate
v = [tex]\sqrt{0.90 \ 2 \ 9.8 \ 4.09 }[/tex]
v = 8.49 m / s
The energy loss must be used before calculating the speed since if it were used afterwards the speed should be multiplied by 0.9 which we can see is incorrect.
In conclusion using the conservation of mechanical energy we can find the result for the velocity of the body when it is under the balcony and has a loss of energy due to friction are:
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