### Physics: Variation of Gravitational Acceleration with ElevationThe acceleration due to gravity, \( g \), is constant at sea level on the Earth's surface. However, this acceleration decreases as an object moves away from the Earth's surface due to the increase in distance from the center of the Earth. #### Derivation of the ExpressionWe are tasked with deriving an expression for the acceleration due to gravity at a distance \( h \) above the Earth's surface, denoted as \( g_h \). We need to express this equation in terms of the Earth's radius \( R \), the gravitational constant at sea level \( g \), and the height \( h \).The derived equation is:\[ g_h = g \left( 1 + \frac{h}{R} \right)^{-2} \]#### Application of the FormulaSuppose a hiker with a mass of 91.75 kg has ascended to a height of \( 1.880 \times 10^3 \) meters (1880 meters) above sea level while climbing Mt. Washington. We need to calculate the percentage change in the hiker's weight from its value at sea level due to climbing to this elevation. The given constants are:- Gravitational acceleration at sea level, \( g = 9.807 \text{ m/s}^2 \)- Radius of the Earth, \( R = 6.371 \times 10^6 \text{ m} \)#### Calculation Steps1. **Determine the gravitational acceleration at the height, \( g_h \)**:\[ g_h = 9.807 \left( 1 + \frac{1880}{6.371 \times 10^6} \right)^{-2} \]2. **Calculate the fractional change in gravity**:\[ \frac{g_h}{g} = \left( 1 + \frac{1880}{6.371 \times 10^6} \right)^{-2} \]3. **Convert to percentage change in weight**:\[ \text{Percentage change in weight} = \left( 1 - \frac{g_h}{g} \right) \times 100 \]Once the student uses the proper values and performs the calculations carefully, they should enter their final answer as a positive value. In the example provided, the student initially entered a weight change of 0%, which is

Name: ### Physics: Variation of Gravitational Acceleration with ElevationTh
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: ### Physics: Variation of Gravitational Acceleration with ElevationThe acceleration due to gravity, \( g \), is constant at sea level on the Earth's surface. However, this acceleration decreases as an object moves away from the Earth's surface due t