To determine the mechanical energy the ball has right before it hits the ground, we need to calculate the potential energy the ball possesses at the given height, as it will convert to kinetic energy just before impact. The formula for gravitational potential energy is given by:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared),
- [tex]\( h \)[/tex] is the height from which the object is dropped (in meters).
Given:
- [tex]\( m = 0.2 \)[/tex] kg,
- [tex]\( g = 9.8 \)[/tex] m/s²,
- [tex]\( h = 10 \)[/tex] m,
we substitute these values into the formula to find the potential energy:
[tex]\[ PE = 0.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 10 \, \text{m} \][/tex]
[tex]\[ PE = 0.2 \times 9.8 \times 10 \][/tex]
[tex]\[ PE = 19.6 \, \text{J} \][/tex]
Therefore, the mechanical energy the ball has right before it hits the ground, assuming no air resistance, is 19.6 joules. Hence, the correct answer is:
B. 19.6 J
