Final answer:
To calculate the potential energy lost, we need to determine the initial potential energy at the top of the hill and subtract the final potential energy at the bottom of the hill. The potential energy lost by the rock is 49000 J.
Step-by-step explanation:
The potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height. In this case, the rock has a mass of 10 kg and rolls down a 500 m hill. To calculate the potential energy lost, we need to determine the initial potential energy at the top of the hill and subtract the final potential energy at the bottom of the hill:
Initial potential energy = mgh = (10 kg)(9.8 m/s²)(500 m) = 49000 J
Final potential energy = mgh = (10 kg)(9.8 m/s²)(0 m) = 0 J
Therefore, the potential energy lost by the rock is 49000 J.