To solve the problem, we need to understand the relationship between the force of gravity on an object and its mass.
Given:
- The force of gravity on an object ([tex]\(F\)[/tex]) varies directly with its mass ([tex]\(m\)[/tex]).
- The constant of variation due to gravity is 32.2 feet per second squared.
In direct variation, the relationship between two variables can be expressed using the equation:
[tex]\[ F = k \cdot m \][/tex]
where [tex]\(F\)[/tex] is the force, [tex]\(k\)[/tex] is the constant of variation (in this case, [tex]\(k = 32.2\)[/tex] ft/s[tex]\(^2\)[/tex]), and [tex]\(m\)[/tex] is the mass of the object.
Substituting the given constant of variation into the equation, we have:
[tex]\[ F = 32.2 \cdot m \][/tex]
This means the force [tex]\(F\)[/tex] can be calculated by multiplying the mass [tex]\(m\)[/tex] by the constant 32.2.
Now, we need to find the correct equation from the given options:
1. [tex]\(F = 16.1 m\)[/tex]
2. [tex]\(F = \frac{16.1}{m^2}\)[/tex]
3. [tex]\(F = 32.2 m\)[/tex]
4. [tex]\(F = \frac{32.2}{m^2}\)[/tex]
From our derived equation, [tex]\( F = 32.2 \cdot m \)[/tex], we observe that the correct corresponding option is:
[tex]\[ F = 32.2 m \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{F = 32.2 m} \][/tex]
