Final answer:
To find the speed of the baseball after being hit by a bat, the work-energy principle is used. The work done by the bat and the potential energy due to the ball's height are considered to compute the ball's final kinetic energy, from which its speed can be found.
Step-by-step explanation:
The question asks to determine the speed of a baseball after it has been struck by a bat, given certain information about the work done by the bat, the mass of the ball, and its initial speed. We'll utilize the work-energy principle, which states that the work done on an object is equal to the change in kinetic energy of the object. Since the bat does work on the ball, this must be taken into account alongside the work done by gravity when the ball is at a height of 25.0 m above the point of impact.
First, we calculate the initial kinetic energy of the ball (KEi) using its initial speed (vi) and mass (m):
KEi = ½mvi2 = ½(0.140 kg)(40.0 m/s)2.
Then, we add the work done by the bat (Wnc) to the initial kinetic energy to get the total energy available after impact (Etotal):
Etotal = KEi + Wnc.
Next, we subtract the gravitational potential energy (PEg) at 25.0 m height to get the kinetic energy after the ball leaves the bat (KEf):
PEg = mgh,
KEf = Etotal - PEg.
Finally, we solve for the final speed of the ball (vf) using KEf:
KEf = ½mvf2
=> vf = √(2KEf/m).
All that remains is to plug in the numbers and calculate the final speed of the ball.