Final answer:
To calculate the gravity on Planet X, the loss of potential energy as the space rock falls is equated to the work done by gravity. Using the formula PE = m * g * h, we find that the gravity is 16 m/s².
Step-by-step explanation:
To find the gravity on Planet X, we can use the relationship between the change in potential energy and the work done by the gravitational force.
When the space rock falls and loses 20 J of energy, this energy loss is equivalent to the work done by gravity as the rock descends 2.5 meters.
We have the formula for gravitational potential energy (PE) as PE = m * g * h, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height.
Since the space rock loses 20 J of energy, we can set that equal to the potential energy formula:
20 J = 0.5 kg * g * 2.5 m
Solving this equation for 'g' gives:
g = 20 J / (0.5 kg * 2.5 m)
g = 16 m/s²
Therefore, the acceleration due to gravity on Planet X is 16 m/s².