Final answer:
The final velocity of a moon rock falling to the surface from 7.8 m would be approximately 5.0 m/s, calculated using the square root of twice the product of gravitational acceleration (1.6 m/s²) and the height (7.8 m). The Moon's lack of atmosphere means there is no air resistance to alter the velocity.
Step-by-step explanation:
To determine the velocity of a moon rock as it strikes the Moon's surface, we use the formula for the final velocity of an object in free fall, given by V = √(2gh), where g is the acceleration due to gravity and h is the height. On the Moon, g is approximately 1.6 m/s² and the height h is 7.8 m. Plugging these values into the formula gives:
V = √(2 * 1.6 m/s² * 7.8 m) = √(24.96 m²/s²) = 4.996 m/s approximately.
The rock's velocity as it strikes the Moon's surface would be about 5.0 m/s. Since the Moon has no atmosphere, there is no air resistance to slow down the rock, so its velocity upon impact would be the same as when it was dropped.