Final answer:
The mass of the ball is calculated using the gravitational potential energy formula GPE = mgh. After substituting the given values (GPE = 46,027 J, g = 10 m/s², h = 883 m), the mass is approximately 5.21 kg, which suggests a typo as the closest option is 4.6 kg (Option A).
Step-by-step explanation:
To find out the mass of the ball, we use the formula for gravitational potential energy (GPE), which is GPE = mgh, where:
- m is the mass,
- g is the acceleration due to gravity, and
- h is the height.
The problem gives us the GPE as 46,027 J, the height (h) as 883 m, and the acceleration due to gravity (g) as 10 m/s². To find the mass (m), we rearrange the formula to m = GPE / (gh), and plug in our known values:
m = 46,027 J / (10 m/s² * 883 m) = 46,027 J / 8,830 m²/s² = 5.21 kg (approximately)
However, since none of the answer choices exactly match, it seems like there may have been rounding in the question or a typo. If we round to the nearest option, we get 4.6 kg, which is option A.