Increasing 69094

The aircraft weighs 61 tons. It climbed from a height of 1000 m to a height of 3000 m while increasing the speed from 170 m/s to 210 m/s. What work did the aircraft engines do?

Correct answer:

W =  1660.42 MJ

Step-by-step explanation:

$$\begin{gathered} m=61\text{t}\to \text{kg}=61\cdot 1000\text{kg}=61000\text{kg} \\ {h}_1=1000\text{m} \\ {h}_2=3000\text{m} \\ {v}_1=170\text{m/s} \\ {v}_2=210\text{m/s} \\ h=h_2-h_1=3000-1000=2000\text{m} \\ g=9.81{\text{m/s}}^2 \\ {E}_1=m\cdot g\cdot h=61000\cdot 9.81\cdot 2000=1196820000\text{J} \\ {E}_2=\frac{1}{2}\cdot m\cdot v_1^2=\frac{1}{2}\cdot 61000\cdot 170^2=881450000\text{J} \\ {E}_3=\frac{1}{2}\cdot m\cdot v_2^2=\frac{1}{2}\cdot 61000\cdot 210^2=1345050000\text{J} \\ K=E_3-E_2=1345050000-881450000=463600000\text{J} \\ E=E_1+K=1196820000+463600000=1660420000\text{J} \\ {W}_1=E\to \text{kJ}=E:1000\text{kJ}=1660420000:1000\text{kJ}=1660420\text{kJ} \\ W=W_1/1000=1660420/1000=\frac{83021}{50}\text{MJ}=1660.42\text{MJ} \end{gathered}$$

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