To determine which planet a person is standing on based on their weight and mass, you can use the formula for weight:
\[ \text{Weight} = \text{Mass} \times \text{Acceleration due to gravity} \]
Given that the person's mass is 85.0 kg and their weight is 305 N, we can rearrange the formula to calculate the acceleration due to gravity on the unknown planet:
\[ \text{Acceleration due to gravity} = \frac{\text{Weight}}{\text{Mass}} \]
Substituting the known values:
\[ \text{Acceleration due to gravity} = \frac{305 , \text{N}}{85.0 , \text{kg}} \approx 3.59 , \text{m/s}^2 \]
Now let's look at the acceleration due to gravity on the given planets:
- Mercury: 3.59 m/s²
- Venus: 8.87 m/s²
- Earth: 9.81 m/s²
- Mars: 3.77 m/s²
Since the calculated acceleration due to gravity is approximately 3.59 m/s², the person is on Mercury.
So the answer is:
a. Mercury