To solve this problem, we need to calculate the kinetic energy (KE) for different masses of a bottle using the given velocity (4 m/s) and the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
We'll calculate the kinetic energy for four different masses: 0.125 kg, 0.250 kg, 0.375 kg, and 0.500 kg.
### Step-by-Step Calculations:
1. When the mass [tex]\( m \)[/tex] is 0.125 kg:
[tex]\[
KE = \frac{1}{2} \times 0.125 \, \text{kg} \times (4 \, \text{m/s})^2
\][/tex]
[tex]\[
KE = \frac{1}{2} \times 0.125 \times 16
\][/tex]
[tex]\[
KE = 1.0 \, \text{J} \, \left(\text{Joules}\right)
\][/tex]
2. When the mass [tex]\( m \)[/tex] is 0.250 kg:
[tex]\[
KE = \frac{1}{2} \times 0.250 \, \text{kg} \times (4 \, \text{m/s})^2
\][/tex]
[tex]\[
KE = \frac{1}{2} \times 0.250 \times 16
\][/tex]
[tex]\[
KE = 2.0 \, \text{J}
\][/tex]
3. When the mass [tex]\( m \)[/tex] is 0.375 kg:
[tex]\[
KE = \frac{1}{2} \times 0.375 \, \text{kg} \times (4 \, \text{m/s})^2
\][/tex]
[tex]\[
KE = \frac{1}{2} \times 0.375 \times 16
\][/tex]
[tex]\[
KE = 3.0 \, \text{J}
\][/tex]
4. When the mass [tex]\( m \)[/tex] is 0.500 kg:
[tex]\[
KE = \frac{1}{2} \times 0.500 \, \text{kg} \times (4 \, \text{m/s})^2
\][/tex]
[tex]\[
KE = \frac{1}{2} \times 0.500 \times 16
\][/tex]
[tex]\[
KE = 4.0 \, \text{J}
\][/tex]
### Summary in Table A:
| Mass (kg) | Kinetic Energy (J) |
|-----------|---------------------|
| 0.125 | 1.0 |
| 0.250 | 2.0 |
| 0.375 | 3.0 |
| 0.500 | 4.0 |
Thus, the kinetic energies for the given masses are as follows:
- For a mass of 0.125 kg, the KE is 1.0 J.
- For a mass of 0.250 kg, the KE is 2.0 J.
- For a mass of 0.375 kg, the KE is 3.0 J.
- For a mass of 0.500 kg, the KE is 4.0 J.
