To determine how high the table is lifted, we can use the formula for gravitational potential energy. The formula is:
[tex]\[ P.E. = m \cdot g \cdot h \][/tex]
where:
- [tex]\( P.E. \)[/tex] is the gravitational potential energy
- [tex]\( m \)[/tex] is the mass of the object
- [tex]\( g \)[/tex] is the acceleration due to gravity
- [tex]\( h \)[/tex] is the height
Given:
- The mass of the table ([tex]\( m \)[/tex]) is [tex]\( 10 \, \text{kg} \)[/tex]
- The increase in gravitational potential energy ([tex]\( P.E. \)[/tex]) is [tex]\( 1470 \, \text{J} \)[/tex]
- The acceleration due to gravity ([tex]\( g \)[/tex]) is [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]
We need to find the height ([tex]\( h \)[/tex]) to which the table is lifted. Rearranging the formula to solve for [tex]\( h \)[/tex] gives:
[tex]\[ h = \frac{P.E.}{m \cdot g} \][/tex]
Substituting the given values into this equation:
[tex]\[ h = \frac{1470 \, \text{J}}{10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2} \][/tex]
[tex]\[ h = \frac{1470}{98} \][/tex]
[tex]\[ h = 15 \, \text{m} \][/tex]
Therefore, the table is lifted to a height of [tex]\( 15 \)[/tex] meters. The correct answer is:
D. 15 m
