At what point in its trajectory does a batted baseball have its minimum speed? if air resistance can be neglected, how does this speed compare with the horizontal component of its velocity at other points?

To understand the problem and give a logical explanation we will use the concepts related to the movement of a Projectile.

On this concept the components concerning the speed of an object that is launched in parabolic motion are characterized. There will be two types of speed components, the vertical and the horizontal.

The vertical component of velocity gradually decreases as it is affected by the force of gravity until it becomes zero at the highest point of the trajectory. After this point, it again begins to increase gradually in effect of its movement towards the gravitational attraction of the Earth.

In the case of horizontal force, if the effect of air resistance is neglected, the speed will be the same throughout the trajectory.

Now comparing this with the movement of the baseball, at the highest point, the vertical component will be zero, and the horizontal velocity will remain. Both at the beginning of the trajectory and at the end of it, there will be components of the vertical velocity, which would increase this value. Therefore the minimum speed value will be at the top, when the vertical component is zero, and the horizontal component is maintained