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Sagot :
To determine which statements are supported by the information provided in the table, let's analyze the kinetic energy of each student. Kinetic energy (KE) is given by the formula:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
From the table, we have the mass and velocity of each student.
1. Calculate the kinetic energy for each student:
- Autumn:
[tex]\[ \text{mass} = 50 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 4 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 400 \, \text{J} \][/tex]
- Mohammed:
[tex]\[ \text{mass} = 57 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 3 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 256.5 \, \text{J} \][/tex]
- Lexy:
[tex]\[ \text{mass} = 53 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 2 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \][/tex]
- Chiang:
[tex]\[ \text{mass} = 64 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 5 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \][/tex]
2. Evaluate each statement:
- Autumn has more kinetic energy than Chiang.
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{J} \][/tex]
Since [tex]\( 400 < 800 \)[/tex], this statement is False.
- Mohammed has less kinetic energy than Autumn.
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{J} \][/tex]
Since [tex]\( 256.5 < 400 \)[/tex], this statement is True.
- Lexy has more kinetic energy than Mohammed.
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{J} \][/tex]
Since [tex]\( 106 < 256.5 \)[/tex], this statement is False.
- Chiang has less kinetic energy than Lexy.
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{J} \][/tex]
Since [tex]\( 800 > 106 \)[/tex], this statement is False.
Therefore, the only statement supported by the information in the chart is:
- Mohammed has less kinetic energy than Autumn.
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
From the table, we have the mass and velocity of each student.
1. Calculate the kinetic energy for each student:
- Autumn:
[tex]\[ \text{mass} = 50 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 4 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 400 \, \text{J} \][/tex]
- Mohammed:
[tex]\[ \text{mass} = 57 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 3 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 256.5 \, \text{J} \][/tex]
- Lexy:
[tex]\[ \text{mass} = 53 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 2 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \][/tex]
- Chiang:
[tex]\[ \text{mass} = 64 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 5 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \][/tex]
2. Evaluate each statement:
- Autumn has more kinetic energy than Chiang.
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{J} \][/tex]
Since [tex]\( 400 < 800 \)[/tex], this statement is False.
- Mohammed has less kinetic energy than Autumn.
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{J} \][/tex]
Since [tex]\( 256.5 < 400 \)[/tex], this statement is True.
- Lexy has more kinetic energy than Mohammed.
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{J} \][/tex]
Since [tex]\( 106 < 256.5 \)[/tex], this statement is False.
- Chiang has less kinetic energy than Lexy.
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{J} \][/tex]
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{J} \][/tex]
Since [tex]\( 800 > 106 \)[/tex], this statement is False.
Therefore, the only statement supported by the information in the chart is:
- Mohammed has less kinetic energy than Autumn.
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