To determine which statements are supported by the information in the chart, we need to calculate the kinetic energy (KE) for each student. The formula for kinetic energy is:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
Let's compute the kinetic energy for each student step-by-step.
1. Kinetic Energy for Autumn:
- Mass = 50 kg
- Velocity = 4 m/s
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 4^2 \][/tex]
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 16 \][/tex]
[tex]\[ KE_{\text{Autumn}} = 25 \times 16 \][/tex]
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{Joules} \][/tex]
2. Kinetic Energy for Mohammed:
- Mass = 57 kg
- Velocity = 3 m/s
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 3^2 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 9 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 28.5 \times 9 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{Joules} \][/tex]
3. Kinetic Energy for Lexy:
- Mass = 53 kg
- Velocity = 2 m/s
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 2^2 \][/tex]
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 4 \][/tex]
[tex]\[ KE_{\text{Lexy}} = 26.5 \times 4 \][/tex]
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{Joules} \][/tex]
4. Kinetic Energy for Chiang:
- Mass = 64 kg
- Velocity = 5 m/s
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 5^2 \][/tex]
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 25 \][/tex]
[tex]\[ KE_{\text{Chiang}} = 32 \times 25 \][/tex]
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{Joules} \][/tex]
Now that we have the kinetic energies:
- KE_{\text{Autumn}} = 400 \, \text{Joules}
- KE_{\text{Mohammed}} = 256.5 \, \text{Joules}
- KE_{\text{Lexy}} = 106 \, \text{Joules}
- KE_{\text{Chiang}} = 800 \, \text{Joules}
Let's evaluate each statement:
1. "Autumn has more kinetic energy than Chiang."
- 400 Joules (Autumn) is less than 800 Joules (Chiang).
- This statement is False.
2. "Mohammed has less kinetic energy than Autumn."
- 256.5 Joules (Mohammed) is less than 400 Joules (Autumn).
- This statement is True.
3. "Lexy has more kinetic energy than Mohammed."
- 106 Joules (Lexy) is less than 256.5 Joules (Mohammed).
- This statement is False.
4. "Chiang has less kinetic energy than Lexy."
- 800 Joules (Chiang) is greater than 106 Joules (Lexy).
- This statement is False.
Therefore, the only statement supported by the information is:
- Mohammed has less kinetic energy than Autumn.
