To find the mass of a ball given its gravitational potential energy, height, and gravitational acceleration, we can use the formula for gravitational potential energy:
[tex]\[ E = m \cdot g \cdot h \][/tex]
where:
- [tex]\( E \)[/tex] is the gravitational potential energy (116.62 J),
- [tex]\( m \)[/tex] is the mass of the ball (what we're trying to find),
- [tex]\( g \)[/tex] is the gravitational acceleration (approximately 9.81 m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height (85 m).
First, we need to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{E}{g \cdot h} \][/tex]
Now, we can plug in the numerical values provided in the question:
The gravitational potential energy [tex]\( E \)[/tex] is 116.62 J.
The height [tex]\( h \)[/tex] is 85 m.
The gravitational acceleration [tex]\( g \)[/tex] is 9.81 m/s[tex]\(^2\)[/tex].
Substituting these values into the equation, we get:
[tex]\[ m = \frac{116.62 \, \text{J}}{9.81 \, \text{m/s}^2 \cdot 85 \, \text{m}} \][/tex]
Evaluating the denominator:
[tex]\[ 9.81 \, \text{m/s}^2 \cdot 85 \, \text{m} = 833.85 \, \text{J/m} \cdot \text{s}^2 \][/tex]
Now divide the numerator by the denominator:
[tex]\[ m = \frac{116.62 \, \text{J}}{833.85 \, \text{J/m} \cdot \text{s}^2} \][/tex]
This gives us approximately:
[tex]\[ m = 0.1398572884811417 \, \text{kg} \][/tex]
Rounding to two decimal places, the mass of the ball is approximately:
[tex]\[ m \approx 0.14 \, \text{kg} \][/tex]
Therefore, the correct answer is:
- 0.14 kg
