A 3.000 kg ball is pitched with a kinetic energy of 20.00 J . The magnitude of the momentum of the ball is
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To find the momentum of the ball, we can use the relationship between kinetic energy (KE) and momentum (p). The kinetic energy is given by the formula: \[ KE = \frac{p^2}{2m} \] where \( m \) is the mass of the ball, and \( p \) is the momentum. Given: - \( KE = 20.00 \, J \) - \( m = 3.000 \, kg \) Rearranging the formula to solve for momentum gives us: \[ p = \sqrt{2 \cdot KE \cdot m} \] Now plugging in the values: \[ p = \sqrt{2 \cdot 20.00 \, J \cdot 3.000 \, kg} \] \[ p = \sqrt{120.00} \] \[ p \approx 10.95 \, kg \cdot m/s \] So, the magnitude of the momentum of the ball is approximately **10.95 kg·m/s**!
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