To determine the kinetic energy of the bowling ball when dropped from different heights, we can use the principle of conservation of energy. The potential energy (PE) at the height from which the ball is dropped will convert to kinetic energy (KE) just before the ball hits the ground.
The potential energy can be calculated using the formula: \[ PE = m \cdot g \cdot h \] Where:
- \( m \) is the mass of the ball (10 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which the ball is dropped (1 m, 2 m, or 3 m).
Calculating the potential energy (and thus kinetic energy just before hitting the ground) for each height:
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For 1 meter: \[ PE = 10 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 1 , \text{m} = 98.1 , \text{J} \]
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For 2 meters: \[ PE = 10 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 2 , \text{m} = 196.2 , \text{J} \]
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For 3 meters: \[ PE = 10 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 3 , \text{m} = 294.3 , \text{J} \]
From these calculations, we observe that the kinetic energy just before hitting the ground will be:
- At 1 meter: 98.1 J
- At 2 meters: 196.2 J
- At 3 meters: 294.3 J
The graph showing the kinetic energy would have the height on the x-axis (1 m, 2 m, and 3 m) and the corresponding kinetic energy on the y-axis (showing 98.1 J, 196.2 J, and 294.3 J).
The correct graph would show a linear relationship with kinetic energy increasing as the height increases. So you should look for a graph with points representing these kinetic energy values increasing with height.