Answer
a. The object falls back to Earth.
b. The object escapes Earth’s gravity and is still moving when it is very far away.
Work Step by Step
If the object’s mechanical energy is zero, its initial positive kinetic energy just balances its negative gravitational potential energy. This is the situation in which the object starts with exactly the escape speed, and ends up very far away, barely moving (zero KE and zero PE).
a. If its mechanical energy is negative, its kinetic energy is insufficient to escape the Earth, and it will eventually fall back to the surface.
b. If its mechanical energy is positive, its kinetic energy is not only sufficient to escape the Earth, but for the object to have some kinetic energy left over when the object is very far from the Earth (when it has zero potential energy).
