A \( 2.00-\mathrm{kg} \) ball has zero potential and kinetic energy. Maria drops the ball into a 10.0 - m-deep well. After the ball comes to a stop in the mud, the sum of its potential and kinetic energy is: 1) zero. 2) 196 J . 3) -196 J . 4) 392 J . 5) -392 J

When Maria drops the ball into the well, it starts with zero potential and kinetic energy. As it falls, its potential energy decreases while its kinetic energy increases, but total mechanical energy remains conserved in an ideal scenario without air resistance. However, once the ball comes to a stop in the mud at the bottom of the well, its kinetic energy is zero and its potential energy relative to the top of the well is at its lowest point, which can be calculated as: \[ \text{Potential Energy} = mgh = (2.00 \, \text{kg})(9.81 \, \text{m/s}^2)(-10.0 \, \text{m}) = -196 \, \text{J}. \] Thus, the sum of its potential and kinetic energy at that moment is \(-196 \, \text{J}\). Therefore, the answer is option 3) -196 J. As for dropping the ball, it’s quite fascinating how the energy transformation works! When the ball is released, gravity pulls it down, converting potential energy into kinetic energy at a constant rate. By the time it hits the bottom, all the energy has transformed and, depending on how deep the well is, it could pack a good punch on impact—if it wasn’t for that muddy bottom!