Answer:
8.21 m/s²
Note: This answer was rounded to three significant figures.
Explanation:
To determine the value of the gravitational acceleration (g) at the astronaut's location, we will use the relationship between weight and gravitational force.
[tex]\boxed{ \begin{array}{ccc} \text{\underline{Weight of an Object:}} \\\\ \vec w = mg \\\\ \text{Where:} \\ \bullet \ \vec w \ \text{is the weight of the object (force due to gravity)} \\ \bullet \ m \ \text{is the mass of the object} \\ \bullet \ g \ \text{is the acceleration due to gravity} \end{array} }[/tex]
We are given:
We want to solve for 'g' using the above equation:
[tex]\Longrightarrow 657 \text{ N}=(80.0 \text{ kg})g[/tex]
[tex]\Longrightarrow g=\dfrac{657 \text{ N}}{80.0 \text{ kg}}[/tex]
[tex]\therefore g \approx \boxed{8.21 \text{m/s}^2}[/tex]
Thus, the value of 'g' at the astronaut's location is approximately 8.21 m/s².