Answer :
To determine which statements are supported by the information provided in the table, we need to calculate the kinetic energy for each student using the formula for kinetic energy:
[tex]\[ \text{Kinetic Energy} (KE) = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
Let's break this down step by step for each student:
1. Autumn:
- Mass = 50 kg
- Velocity = 4 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 0.5 \times 50 \times 16 = 400\, \text{Joules} \][/tex]
2. Mohammed:
- Mass = 57 kg
- Velocity = 3 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 0.5 \times 57 \times 9 = 256.5\, \text{Joules} \][/tex]
3. Lexy:
- Mass = 53 kg
- Velocity = 2 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 0.5 \times 53 \times 4 = 106\, \text{Joules} \][/tex]
4. Chiang:
- Mass = 64 kg
- Velocity = 5 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 0.5 \times 64 \times 25 = 800\, \text{Joules} \][/tex]
The resulting kinetic energies are:
- Autumn: 400 Joules
- Mohammed: 256.5 Joules
- Lexy: 106 Joules
- Chiang: 800 Joules
Now, let's evaluate each statement:
1. Autumn has more kinetic energy than Chiang.
- False. Autumn has 400 Joules, while Chiang has 800 Joules.
2. Mohammed has less kinetic energy than Autumn.
- True. Mohammed has 256.5 Joules, while Autumn has 400 Joules.
3. Lexy has more kinetic energy than Mohammed.
- False. Lexy has 106 Joules, while Mohammed has 256.5 Joules.
4. Chiang has less kinetic energy than Lexy.
- False. Chiang has 800 Joules, while Lexy has 106 Joules.
Therefore, the correct statement supported by the information in the chart is:
- Mohammed has less kinetic energy than Autumn.
[tex]\[ \text{Kinetic Energy} (KE) = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
Let's break this down step by step for each student:
1. Autumn:
- Mass = 50 kg
- Velocity = 4 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 0.5 \times 50 \times 16 = 400\, \text{Joules} \][/tex]
2. Mohammed:
- Mass = 57 kg
- Velocity = 3 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 0.5 \times 57 \times 9 = 256.5\, \text{Joules} \][/tex]
3. Lexy:
- Mass = 53 kg
- Velocity = 2 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 0.5 \times 53 \times 4 = 106\, \text{Joules} \][/tex]
4. Chiang:
- Mass = 64 kg
- Velocity = 5 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 0.5 \times 64 \times 25 = 800\, \text{Joules} \][/tex]
The resulting kinetic energies are:
- Autumn: 400 Joules
- Mohammed: 256.5 Joules
- Lexy: 106 Joules
- Chiang: 800 Joules
Now, let's evaluate each statement:
1. Autumn has more kinetic energy than Chiang.
- False. Autumn has 400 Joules, while Chiang has 800 Joules.
2. Mohammed has less kinetic energy than Autumn.
- True. Mohammed has 256.5 Joules, while Autumn has 400 Joules.
3. Lexy has more kinetic energy than Mohammed.
- False. Lexy has 106 Joules, while Mohammed has 256.5 Joules.
4. Chiang has less kinetic energy than Lexy.
- False. Chiang has 800 Joules, while Lexy has 106 Joules.
Therefore, the correct statement supported by the information in the chart is:
- Mohammed has less kinetic energy than Autumn.
