f the variation of the acceleration of gravity, in m/s2, with elevation z, in m, above
sea level is g = 9.81 − (3.3 × 10−6)z, determine the percent change in weight of an
airliner landing from a cruising altitude of 10 km on a runway at sea level.

We are asked to determine the percent change in weight of an airliner landing from a cruising altitude of 10 km (10,000 m) on a runway at sea level, taking into account the variation in gravitational acceleration with elevation.

### Given:
- Gravitational acceleration formula as a function of height:  
  \[
  g(z) = 9.81 - (3.3 \times 10^{-6})z \, \text{m/s}^2
  \]
- At sea level (\( z = 0 \)):  
  \[
  g(0) = 9.81 \, \text{m/s}^2
  \]
- At cruising altitude (\( z = 10,000 \, \text{m} \)):  
  \[
  g(10,000) = 9.81 - (3.3 \times 10^{-6} \times 10,000)
  \]

### Step 1: Calculate \( g(10,000) \)
\[
g(10,000) = 9.81 - 0.033 = 9.777 \, \text{m/s}^2
\]

### Step 2: Weight formula
Weight \( W \) is given by the formula:
\[
W = mg
\]
where \( m \) is the mass and \( g \) is the gravitational acceleration. The percent change in weight is due to the change in \( g \).

### Step 3: Percent change in weight
The percent change in weight as the airliner descends from 10,000 m to sea level is given by:
\[
\text{Percent change} = \left( \frac{g(0) - g(10,000)}{g(10,000)} \right) \times 100
\]

Substitute the values:
\[
\text{Percent change} = \left( \frac{9.81 - 9.777}{9.777} \right) \times 100
\]
\[
\text{Percent change} = \left( \frac{0.033}{9.777} \right) \times 100 \approx 0.337%
\]

### Conclusion:
The airliner's weight increases by approximately **0.337%** when it descends from a cruising altitude of 10 km to sea level.

Do you need further details or have any questions?

Here are 5 related questions:
1. How does gravity vary with altitude in general?
2. What factors affect the weight of an object besides gravitational changes?
3. How does Earth's shape influence gravitational acceleration at different points?
4. What is the difference between mass and weight?
5. How would this calculation differ if we considered a higher altitude, like 30 km?

**Tip:** Remember, weight depends on gravitational force, but mass remains constant regardless of altitude or location!

The variation of the acceleration of gravity, in m/s², with elevation z, in m, above sea level is g = 9.81 − (3.3 × 10⁻⁶)z. Determine the percent change in weight of an airliner landing from a cruising altitude of 10 km on a runway at sea level.

Calculate the percent change in weight of an airliner descending from 10,000 m to sea level, considering gravitational acceleration. The problem involves algebra and gravitational physics, using formulas like g(z) = 9.81 - (3.3 × 10⁻⁶)z and weight W = mg. Suitable for high school students in Grades 10-12.

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