Mechanical 83220

An airplane weighing 100 tons flies at an altitude of 11 km at a speed of 850 km/h. What is its kinetic, potential, and total mechanical energy?

Correct answer:

E₁ =  2787.4228 MJ
E₂ =  10791 MJ
E₃ =  13578.4228 MJ

Step-by-step explanation:

$$\begin{gathered} m=100\text{t}\to \text{kg}=100\cdot 1000\text{kg}=100000\text{kg} \\ h=11\text{km}\to \text{m}=11\cdot 1000\text{m}=11000\text{m} \\ v=850\text{km/h}\to \text{m/s}=850:3.6\text{m/s}=236.11111\text{m/s} \\ g=9.81{\text{m/s}}^2 \\ kineticenergy \\ {e}_1=\frac{1}{2}\cdot m\cdot v^2=\frac{1}{2}\cdot 100000\cdot 236.1111^2\doteq 2787422839.5062\text{J} \\ {E}_1=e_1/10^6=2787422839.5062/10^6=2787.4228\text{MJ} \end{gathered}$$

$$\begin{gathered} potencialenergy \\ {e}_2=m\cdot g\cdot h=100000\cdot 9.81\cdot 11000=10791000000\text{J} \\ {E}_2=e_2/10^6=10791000000/10^6=10791\text{MJ} \end{gathered}$$

$E_3=E_1+E_2=2787.4228+10791=13578.4228\text{MJ}$

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