Question
Calculate the kinetic energy, in Joules, possessed in each of the following scenarios and match with the correct answer. K.E. = 1/2 m v2 **Not all answers may be used. (16 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 0.5 kg hockey sliding at 2 m/s 75 kg man walking at 1.0 m/s. 75 kg man running at 5.0 m/s. 2000 kg Lamborghini cruising at 30 m/s
Answers
GPT-4o mini
To calculate the kinetic energy (K.E.) for each scenario, we can use the formula:
\[ K.E. = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass (in kg)
- \( v \) is the velocity (in m/s)
Let's calculate the kinetic energy for each scenario:
1. **0.5 kg hockey sliding at 2 m/s**:
\[ K.E. = \frac{1}{2} (0.5 \, \text{kg}) (2 \, \text{m/s})^2 = \frac{1}{2} (0.5) (4) = 1 \, \text{J} \]
2. **75 kg man walking at 1.0 m/s**:
\[ K.E. = \frac{1}{2} (75 \, \text{kg}) (1.0 \, \text{m/s})^2 = \frac{1}{2} (75) (1) = 37.5 \, \text{J} \]
3. **75 kg man running at 5.0 m/s**:
\[ K.E. = \frac{1}{2} (75 \, \text{kg}) (5.0 \, \text{m/s})^2 = \frac{1}{2} (75) (25) = 937.5 \, \text{J} \]
4. **2000 kg Lamborghini cruising at 30 m/s**:
\[ K.E. = \frac{1}{2} (2000 \, \text{kg}) (30 \, \text{m/s})^2 = \frac{1}{2} (2000) (900) = 900000 \, \text{J} \]
### Summary of Kinetic Energies:
- 0.5 kg hockey sliding at 2 m/s = **1 J**
- 75 kg man walking at 1.0 m/s = **37.5 J**
- 75 kg man running at 5.0 m/s = **937.5 J**
- 2000 kg Lamborghini cruising at 30 m/s = **900000 J**
You can match these calculated kinetic energies with the provided responses accordingly.
\[ K.E. = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass (in kg)
- \( v \) is the velocity (in m/s)
Let's calculate the kinetic energy for each scenario:
1. **0.5 kg hockey sliding at 2 m/s**:
\[ K.E. = \frac{1}{2} (0.5 \, \text{kg}) (2 \, \text{m/s})^2 = \frac{1}{2} (0.5) (4) = 1 \, \text{J} \]
2. **75 kg man walking at 1.0 m/s**:
\[ K.E. = \frac{1}{2} (75 \, \text{kg}) (1.0 \, \text{m/s})^2 = \frac{1}{2} (75) (1) = 37.5 \, \text{J} \]
3. **75 kg man running at 5.0 m/s**:
\[ K.E. = \frac{1}{2} (75 \, \text{kg}) (5.0 \, \text{m/s})^2 = \frac{1}{2} (75) (25) = 937.5 \, \text{J} \]
4. **2000 kg Lamborghini cruising at 30 m/s**:
\[ K.E. = \frac{1}{2} (2000 \, \text{kg}) (30 \, \text{m/s})^2 = \frac{1}{2} (2000) (900) = 900000 \, \text{J} \]
### Summary of Kinetic Energies:
- 0.5 kg hockey sliding at 2 m/s = **1 J**
- 75 kg man walking at 1.0 m/s = **37.5 J**
- 75 kg man running at 5.0 m/s = **937.5 J**
- 2000 kg Lamborghini cruising at 30 m/s = **900000 J**
You can match these calculated kinetic energies with the provided responses accordingly.