To determine the mass of the ball using the given gravitational potential energy and height, we will use the formula for gravitational potential energy:
[tex]\[ E_p = m \cdot g \cdot h \][/tex]
where:
- [tex]\( E_p \)[/tex] is the gravitational potential energy,
- [tex]\( m \)[/tex] is the mass of the ball,
- [tex]\( g \)[/tex] is the acceleration due to gravity, and
- [tex]\( h \)[/tex] is the height.
Given:
- Gravitational potential energy ([tex]\( E_p \)[/tex]) = 116.62 Joules,
- Height ([tex]\( h \)[/tex]) = 85 meters,
- Acceleration due to gravity ([tex]\( g \)[/tex]) is approximately 9.81 m/s².
We need to find the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for mass:
[tex]\[ m = \frac{E_p}{g \cdot h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{116.62}{9.81 \cdot 85} \][/tex]
Let's calculate the right-hand side to find the mass of the ball. After computing, we find that the mass of the ball is:
[tex]\[ m \approx 0.14 \, \text{kg} \][/tex]
So, the mass of the ball is approximately 0.14 kg.
Thus, the correct option amongst the choices provided is:
[tex]\[ \boxed{0.14 \, \text{kg}} \][/tex]
