Certainly! Let's walk through the problem step by step to determine the kinetic energy of the apple at the height of 1.5 meters.
### Step 1: Given Values
- Mass of the apple, [tex]\( m = 0.5 \)[/tex] kilograms
- Initial height, [tex]\( h_i = 2 \)[/tex] meters
- Final height, [tex]\( h_f = 1.5 \)[/tex] meters
- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] meters per second squared
### Step 2: Calculate the Potential Energy at the Initial Height
The potential energy (PE) at a height [tex]\( h \)[/tex] is given by the formula:
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
So, at the initial height of 2 meters:
[tex]\[ \text{PE}_{\text{initial}} = 0.5 \times 9.8 \times 2 \][/tex]
[tex]\[ \text{PE}_{\text{initial}} = 9.8 \ \text{Joules} \][/tex]
### Step 3: Calculate the Potential Energy at the Final Height
Using the same formula for potential energy, we calculate the potential energy at the final height of 1.5 meters:
[tex]\[ \text{PE}_{\text{final}} = 0.5 \times 9.8 \times 1.5 \][/tex]
[tex]\[ \text{PE}_{\text{final}} = 7.35 \ \text{Joules} \][/tex]
### Step 4: Determine the Kinetic Energy at the Final Height
The kinetic energy (KE) at the final height can be found by the difference in potential energy at the initial and final heights. The loss in potential energy gets converted into kinetic energy:
[tex]\[ \text{KE} = \text{PE}_{\text{initial}} - \text{PE}_{\text{final}} \][/tex]
[tex]\[ \text{KE} = 9.8 - 7.35 \][/tex]
[tex]\[ \text{KE} = 2.45 \ \text{Joules} \][/tex]
Thus, the kinetic energy of the apple at the height of 1.5 meters is [tex]\( 2.45 \ \text{Joules} \)[/tex].
### Final Answer
[tex]\[ 2.45 \ \text{J} \][/tex]
Therefore, the correct option is:
[tex]\[ \$2.45 \ J \][/tex]
