To determine which graph accurately reflects the relationship between height and potential energy for a 200 kg man based on the provided data, we first need to analyze the relationship.
The potential energy (PE) can be calculated using the formula: \[ \text{PE} = m \times g \times h \] where:
- \( m \) is the mass (200 kg),
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s²),
- \( h \) is the height in meters.
Given:
- At 100 meters, potential energy is 50 Joules.
- At 200 meters, potential energy is 100 Joules.
- At 300 meters, potential energy is 150 Joules.
The key observation is that as height increases, the potential energy increases, but the increase in potential energy is not linear (it appears to be consistent in this dataset), suggesting a linear relation with the data provided.
- At 100 meters, PE = 50 Joules.
- At 200 meters, PE = 100 Joules.
- At 300 meters, PE = 150 Joules.
From that data, we can see:
- The potential energy increases by 50 Joules for every increase of 100 meters in height.
Thus, the relationship is a straight line that starts from the origin (0,0) and has a constant slope.
Now, to choose the correct graph from the provided options (Grade 8 Science_Unit 2_Q2A, Q2B, Q2C, Q2D), look for the graph that displays a straight line starting from the origin, increasing steadily.
Without seeing the actual graphs, I recommend you look for one that shows this consistent linear increase with height for potential energy. If you can provide descriptions of the graphs, I'd be happy to help you identify the correct one!
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