Final answer:
The height of the hillside where the dog is sitting is calculated to be 4 meters, based on the given potential energy and the mass of the dog.
Step-by-step explanation:
To calculate the height of the hillside that the dog is sitting on, we can use the formula for gravitational potential energy (PE), which is PE = mgh, where m is mass, g is the acceleration due to gravity (9.81 m/s² on Earth's surface), and h is the height above the ground. Given that the potential energy (PE) is 1,568 J and the mass (m) of the dog is 40 kg, we can rearrange the formula to solve for the height h as follows:
h = PE / (mg)
Where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
- h is the height of the hillside
Substitute the given values:
h = 1,568 J / (40 kg * 9.81 m/s²)
h = 1,568 J / 392.4 kg*m/s²
h = 4 m
Therefore, the height of the hillside is 4 meters.