To find the planet on which a person weighing 305 N has a mass of 85.0 kg, we can use the formula for weight:
\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \]
Given:
- Weight = 305 N
- Mass = 85.0 kg
We can rearrange this formula to find the acceleration due to gravity on that planet:
\[ \text{acceleration due to gravity} = \frac{\text{Weight}}{\text{mass}} = \frac{305 , \text{N}}{85.0 , \text{kg}} \]
Now let's calculate it:
\[ \text{acceleration due to gravity} = \frac{305}{85.0} \approx 3.59 , \text{m/s}^2 \]
Now, we compare this value with 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 of approximately 3.59 m/s² matches that of Mercury, the person is located on Mercury.