To calculate the total energy of the watermelon at the moment it is thrown, we need to consider both its gravitational potential energy and its kinetic energy.
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Gravitational Potential Energy (PE): \[ PE = mgh \] where:
- \( m = 1.4 , \text{kg} \) (mass of the watermelon)
- \( g = 9.81 , \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 10 , \text{m} \) (height above ground)
Plugging in the values: \[ PE = 1.4 , \text{kg} \times 9.81 , \text{m/s}^2 \times 10 , \text{m} = 137.4 , \text{J} \]
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Kinetic Energy (KE): \[ KE = \frac{1}{2}mv^2 \] where:
- \( v = 8 , \text{m/s} \) (initial velocity given)
Plugging in the values: \[ KE = \frac{1}{2} \times 1.4 , \text{kg} \times (8 , \text{m/s})^2 = \frac{1}{2} \times 1.4 , \text{kg} \times 64 , \text{m}^2/\text{s}^2 = 44.8 , \text{J} \]
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Total Energy (TE): Total Energy is the sum of Potential Energy and Kinetic Energy. \[ TE = PE + KE \] \[ TE = 137.4 , \text{J} + 44.8 , \text{J} = 182.2 , \text{J} \]
Thus, the total energy of the watermelon is approximately 182 J.
The closest answer from your options is 182 J.
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