To determine how much less force a vacationer would be applying to their joints when walking on Mars compared to Earth, we can use the ratio of gravitational accelerations on the two planets.
- Gravitational acceleration on Earth (g_E) = 9.8 m/s²
- Gravitational acceleration on Mars (g_M) = 3.7 m/s²
The force exerted on the joints due to gravity is proportional to the gravitational acceleration. Thus, the ratio of the forces (and hence the impact on joints) can be calculated as follows:
\[ \text{Force Ratio} = \frac{g_E}{g_M} = \frac{9.8}{3.7} \]
Now, we can calculate this ratio:
\[ \text{Force Ratio} = 2.64864864865 \]
Rounding this to two decimal places gives approximately 2.65.
This means the vacationer would be applying about 2.65 times less force to their joints when walking on Mars compared to walking on Earth.
Based on the options provided, the closest option is:
2.6 times less force.