Answer :
To calculate the potential energy gained by the ball, we can use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity in meters per second squared (m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height in meters (m) that the object is raised.
Let's plug the values into the formula:
- The mass [tex]\( m \)[/tex] of the ball is 8.5 kg.
- The acceleration due to gravity [tex]\( g \)[/tex] is 9.81 m/s[tex]\(^2\)[/tex].
- The height [tex]\( h \)[/tex] is 16 m.
Now substitute these values into the formula:
[tex]\[ \text{Potential Energy} = 8.5 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 16 \, \text{m} \][/tex]
By performing the multiplication:
[tex]\[ \text{Potential Energy} = 8.5 \times 9.81 \times 16 \][/tex]
When you calculate this, you will find:
[tex]\[ \text{Potential Energy} = 1334.16 \, \text{Joules (J)} \][/tex]
Thus, the potential energy gained by the ball is approximately 1334 J, which rounds to option c, [tex]\( \quad 1,334 \, \text{J} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity in meters per second squared (m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height in meters (m) that the object is raised.
Let's plug the values into the formula:
- The mass [tex]\( m \)[/tex] of the ball is 8.5 kg.
- The acceleration due to gravity [tex]\( g \)[/tex] is 9.81 m/s[tex]\(^2\)[/tex].
- The height [tex]\( h \)[/tex] is 16 m.
Now substitute these values into the formula:
[tex]\[ \text{Potential Energy} = 8.5 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 16 \, \text{m} \][/tex]
By performing the multiplication:
[tex]\[ \text{Potential Energy} = 8.5 \times 9.81 \times 16 \][/tex]
When you calculate this, you will find:
[tex]\[ \text{Potential Energy} = 1334.16 \, \text{Joules (J)} \][/tex]
Thus, the potential energy gained by the ball is approximately 1334 J, which rounds to option c, [tex]\( \quad 1,334 \, \text{J} \)[/tex].
