find the mass of a ball on a roof 30 meters high, if the ball's gravitational energy is 58.8 joules.

3.92kg

To find the mass of the ball on a roof, we can use the gravitational potential energy equation:

Gravitational Potential Energy (GPE) = mass (m) * gravitational acceleration (g) * height (h)

Given:
GPE = 58.8 joules
Height (h) = 30 meters
Gravitational acceleration (g) on Earth is approximately 9.8 m/s^2

Substituting the values into the equation:
58.8 J = m * 9.8 m/s^2 * 30 m

Now, let's solve for the mass (m):

First, divide both sides of the equation by (9.8 m/s^2 * 30 m) to isolate the mass:
58.8 J / (9.8 m/s^2 * 30 m) = m

Using a calculator:
58.8 J / (9.8 m/s^2 * 30 m) ≈ 0.2 kg

Therefore, the mass of the ball on the roof is approximately 0.2 kilograms.