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Sagot :
To solve this problem, we need to calculate the kinetic energy of each student. The formula for kinetic energy (KE) is given by:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{speed}^2 \][/tex]
We'll use this formula for each student.
### Calculations
1. Autumn:
- Mass: 50 kg
- Speed: 4 m/s
- Kinetic Energy: [tex]\( KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 4^2 = \frac{1}{2} \times 50 \times 16 = 400 \, \text{J} \)[/tex]
2. Mohammed:
- Mass: 57 kg
- Speed: 3 m/s
- Kinetic Energy: [tex]\( KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 3^2 = \frac{1}{2} \times 57 \times 9 = 256.5 \, \text{J} \)[/tex]
3. Lexy:
- Mass: 53 kg
- Speed: 2 m/s
- Kinetic Energy: [tex]\( KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 2^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \)[/tex]
4. Chiang:
- Mass: 64 kg
- Speed: 5 m/s
- Kinetic Energy: [tex]\( KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 5^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \)[/tex]
### Evaluating Statements:
1. Autumn has more kinetic energy than Chiang.
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( 400 \text{ J} < 800 \text{ J} \)[/tex], so this statement is False.
2. Mohammed has less kinetic energy than Autumn.
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( 256.5 \text{ J} < 400 \text{ J} \)[/tex], so this statement is True.
3. Lexy has more kinetic energy than Mohammed.
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( 106 \text{ J} < 256.5 \text{ J} \)[/tex], so this statement is False.
4. Chiang has less kinetic energy than Lexy.
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( 800 \text{ J} > 106 \text{ J} \)[/tex], so this statement is False.
Based on these calculations, the statement supported by the information in the chart is:
"Mohammed has less kinetic energy than Autumn."
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{speed}^2 \][/tex]
We'll use this formula for each student.
### Calculations
1. Autumn:
- Mass: 50 kg
- Speed: 4 m/s
- Kinetic Energy: [tex]\( KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 4^2 = \frac{1}{2} \times 50 \times 16 = 400 \, \text{J} \)[/tex]
2. Mohammed:
- Mass: 57 kg
- Speed: 3 m/s
- Kinetic Energy: [tex]\( KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 3^2 = \frac{1}{2} \times 57 \times 9 = 256.5 \, \text{J} \)[/tex]
3. Lexy:
- Mass: 53 kg
- Speed: 2 m/s
- Kinetic Energy: [tex]\( KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 2^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \)[/tex]
4. Chiang:
- Mass: 64 kg
- Speed: 5 m/s
- Kinetic Energy: [tex]\( KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 5^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \)[/tex]
### Evaluating Statements:
1. Autumn has more kinetic energy than Chiang.
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( 400 \text{ J} < 800 \text{ J} \)[/tex], so this statement is False.
2. Mohammed has less kinetic energy than Autumn.
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( 256.5 \text{ J} < 400 \text{ J} \)[/tex], so this statement is True.
3. Lexy has more kinetic energy than Mohammed.
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( 106 \text{ J} < 256.5 \text{ J} \)[/tex], so this statement is False.
4. Chiang has less kinetic energy than Lexy.
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( 800 \text{ J} > 106 \text{ J} \)[/tex], so this statement is False.
Based on these calculations, the statement supported by the information in the chart is:
"Mohammed has less kinetic energy than Autumn."
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