To determine which planet the person is standing on, we can use the formula for weight, which is given by:
\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \]
Given:
- Mass of the person = 85.0 kg
- Weight = 305 N
We can find the acceleration due to gravity on that planet by rearranging the formula:
\[ \text{acceleration due to gravity} = \frac{\text{Weight}}{\text{mass}} \]
Now, substituting the values:
\[ \text{acceleration due to gravity} = \frac{305 , \text{N}}{85.0 , \text{kg}} \approx 3.59 , \text{m/s}^2 \]
Now, we can compare this value to the typical acceleration due to gravity on the different planets:
- Mars: approximately \(3.71 , \text{m/s}^2\)
- Earth: approximately \(9.81 , \text{m/s}^2\)
- Mercury: approximately \(3.7 , \text{m/s}^2\)
- Venus: approximately \(8.87 , \text{m/s}^2\)
Since \(3.59 , \text{m/s}^2\) doesn't match those exactly but is quite close to Mars and Mercury, it suggests that the weight calculation may be influenced by rounding or variations.
However, the value \(3.59 , \text{m/s}^2\) is closest to the acceleration due to gravity on Mars. Therefore, it is likely that the person is standing on:
a. Mars