Answer:
E_{k2}=2660 [J] kinetic energy.
Explanation:
The energy in the initial state i.e. when the rollercoaster is at the top is equal to the energy in the final state i.e. when it is at the bottom of the hill.
These states can be represented by means of the second equation.
Since the rollercoaster is located in the bottom of the hill where the potential energy level is zero, therefore there is only kinetic energy in the second state.
In empty space probably means, there is no force on the ball.
(This assumption is not quite correct since there is still the force of gravity between the ball and the astronaut, but this force is very very small and can be neglected.)
Assuming there is no force on the ball, Newtown's 1st law says: When viewed in an internal frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
This means:
If there is no force on the ball, there will be no acceleration on the ball either.
If the acceleration is zero, the velocity of the ball never changes.