A baseball catcher applies a rightward force of 6000n to a leftward moving baseball to bring it from a high speed to a rest position over a distance of 0.10metres. If the ball begins with 605 j of energy , then the final or total mechanical energy in joules is?

By "mechanical energy" I assume you mean the sum of potential and kinetic energy. The KE of an object is dependent on its mass and velocity:



So once the baseball has been caught and is at rest, its velocity is 0, right? So it should be obvious what its KE is at that point.

The balls' potential energy gain is dependent on the mass and height the ball moves upward:



(at the earth's surface). In this problem there is nothing about the ball moving upward, so assume .