Final answer:
Without the ball's mass or velocity at the bottom of the ramp, it's not possible to calculate the correct kinetic energy among the provided options. Conservation of mechanical energy principles would be used if the required information were available.
Step-by-step explanation:
To determine the ball's kinetic energy as it rolls through the velocimeter at the bottom of the ramp, we need to apply the principles of physics, specifically the concept of conservation of mechanical energy assuming no non-conservative forces are doing work (like air resistance or friction, which the question suggests we ignore).
The ball's gravitational potential energy at the top of the hill converts to kinetic energy as the ball rolls down the hill. The total mechanical energy of the system remains constant if there's no friction, meaning the potential energy at the top is equal to kinetic energy at the bottom.
The gravitational potential energy (PE) of the ball at the top of the hill can be calculated using the formula
PE = mgh,
where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the hill.
The kinetic energy (KE) at the bottom is given by KE = 0.5 * m * v^2, where v is the velocity.
However, the question does not provide the mass of the ball or its velocity at the bottom of the ramp, making it impossible to calculate the kinetic energy with the data given.
Therefore, without further information, we are unable to provide one of the multiple-choice answers listed (0.18 J, 0.45 J, 0.54 J, 0.27 J) as the correct kinetic energy of the rolling ball.