To compare the kinetic and potential energies of the two watermelons, we can use the following formulas:
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Kinetic Energy (KE): \[ KE = \frac{1}{2}mv^2 \] where \( m \) is the mass and \( v \) is the speed.
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Potential Energy (PE): \[ PE = mgh \] where \( h \) is the height above the ground, \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)), and \( m \) is the mass.
Given Data:
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Watermelon A:
- Mass = 4 kg
- Speed = 2 m/s
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Watermelon B:
- Mass = 4 kg
- Speed = 4 m/s
Calculating Kinetic Energies:
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Kinetic Energy of Watermelon A: \[ KE_A = \frac{1}{2} \times 4 , \text{kg} \times (2 , \text{m/s})^2 = \frac{1}{2} \times 4 \times 4 = 8 , \text{J} \]
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Kinetic Energy of Watermelon B: \[ KE_B = \frac{1}{2} \times 4 , \text{kg} \times (4 , \text{m/s})^2 = \frac{1}{2} \times 4 \times 16 = 32 , \text{J} \]
Conclusion about Kinetic Energies:
- Watermelon A has 8 J of kinetic energy.
- Watermelon B has 32 J of kinetic energy.
- Therefore, Watermelon B has more kinetic energy than Watermelon A.
Potential Energies:
Both watermelons, when falling from the same height, will have the same potential energy if they have the same mass and are at the same initial height. Thus, their potential energy will depend on the height \( h \) from which they fall. So if both fall from the same height:
- PE_A = PE_B
Final Comparison:
- Kinetic Energy: Watermelon B has more kinetic energy than Watermelon A.
- Potential Energy: Assuming they start from the same height, both would have the same potential energy.
Thus, the appropriate comparison of kinetic and potential energies in this context would be:
The watermelon A has less kinetic energy than watermelon B.
However, based on the available options, the conclusion is:
The watermelon A has more kinetic energy is incorrect. The correct answer is: Both fruits have the same potential energy if they are dropped from the same height, but watermelon B has more kinetic energy.
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