Mechanical energy

A stone with a mass of 2 kg falls in free fall from a tower with a height of 80 m. What is its kinetic energy, and what is its potential energy:

a) At the beginning of the fall,
b) In 1 s from the beginning of the fall,
c) Upon impact,
d) What is its mechanical energy relative to the Earth's surface during the fall?

Final Answer:

E₁ =  0 J
E₂ =  100 J
E₃ =  1600 J
E₄ =  1600 J

Step-by-step explanation:

$$\begin{gathered} m=2\text{kg} \\ h=80\text{m} \\ g=10{\text{m/s}}^2 \\ {v}_1=0\text{m/s} \\ {E}_1=\frac{1}{2}\cdot m\cdot v_1^2=\frac{1}{2}\cdot 2\cdot 0^2=0\text{J} \end{gathered}$$

$$\begin{gathered} t_2=1\text{s} \\ {v}_2=g\cdot t_2=10\cdot 1=10\text{m/s} \\ {E}_2=\frac{1}{2}\cdot m\cdot v_2^2=\frac{1}{2}\cdot 2\cdot 10^2=100\text{J} \end{gathered}$$

$$\begin{gathered} v_3=\sqrt{2\cdot g\cdot h}=\sqrt{2\cdot 10\cdot 80}=40\text{m/s} \\ {E}_3=\frac{1}{2}\cdot m\cdot v_3^2=\frac{1}{2}\cdot 2\cdot 40^2=1600\text{J} \end{gathered}$$

$E_4=m\cdot g\cdot h=2\cdot 10\cdot 80=1600\text{J}$

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