A 1.00 x 10 4 kg airplane lands, descending a vertical distance of 10.0 km while travelling 100.

km measured along the ground. What is the plane&#39;s loss of potential energy?

To calculate the plane's loss of potential energy, we can use the formula for gravitational potential energy (GPE):

\[
\Delta \text{GPE} = m \cdot g \cdot \Delta h
\]

Where:
- \( m \) is the mass of the airplane \( = 1.00 \times 10^4 \, \text{kg} \),
- \( g \) is the acceleration due to gravity \( \approx 9.81 \, \text{m/s}^2 \),
- \( \Delta h \) is the vertical distance the plane descends \( = 10.0 \, \text{km} = 10,000 \, \text{m} \).

Let's calculate the loss in potential energy.The plane's loss of potential energy as it descends 10.0 km is \( 981,000,000 \, \text{J} \) or \( 9.81 \times 10^8 \, \text{J} \).

Would you like further details or have any questions?

Here are five related questions to consider:
1. How does the plane's kinetic energy change as it loses potential energy during descent?
2. What would happen to the potential energy if the plane descended only half the vertical distance?
3. How would the potential energy loss differ on a planet with lower gravity?
4. How does the angle of descent (relative to the ground) affect the calculation of potential energy loss?
5. What other factors could influence the total energy of the plane during descent?

**Tip:** When dealing with problems involving energy, it's essential to consider all forms of energy, including potential, kinetic, and any work done by or against forces, to understand the total energy transformation in the system.

Learn how to calculate the loss of potential energy of a 1.00 × 10^4 kg airplane as it descends a vertical distance of 10.0 km. Detailed step-by-step solution using the gravitational potential energy formula. Suitable for advanced high school students.

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