To determine the height to which a 6 kg weight is lifted given its gravitational potential energy is 70.56 Joules and the acceleration due to gravity is [tex]\( g = 9.8 \, m/s^2 \)[/tex], we can use the formula for gravitational potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height.
We need to solve for [tex]\( h \)[/tex]. Rearranging the formula to solve for height gives:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]
Given:
- [tex]\( PE = 70.56 \, J \)[/tex]
- [tex]\( m = 6 \, kg \)[/tex]
- [tex]\( g = 9.8 \, m/s^2 \)[/tex]
Substitute these values into the equation to find the height:
[tex]\[ h = \frac{70.56 \, J}{6 \, kg \cdot 9.8 \, m/s^2} \][/tex]
Calculate [tex]\( 6 \, kg \cdot 9.8 \, m/s^2 \)[/tex]:
[tex]\[ 6 \cdot 9.8 = 58.8 \, kg \cdot m/s^2 \][/tex]
Now, substitute and divide:
[tex]\[ h = \frac{70.56 \, J}{58.8 \, kg \cdot m/s^2} \][/tex]
[tex]\[ h = 1.2 \, m \][/tex]
Therefore, the height is [tex]\( 1.2 \, m \)[/tex].
Thus, the correct answer is:
D. [tex]\( 1.2 \, m \)[/tex]
