If a ball is thrown with an initial horizontal and vertical velocity. What is the VERTICAL velocity at the highest point? *

Answer 1

It's also in my answer on your follow up question.

With these kind of problems and most of physics problems, you should make a sketch of the situation.

Draw the path of the ball. Draw free-body diagrams of the ball in different locations.

What forces are acting on the ball?

If air resistance is neglected, which is often the case in these kind of situations, the only force acting on the ball is gravity F_g.

It pulls on the ball towards the center of the earth.

A ball thrown upwards will be slowed down until it reaches its highest point, then get accelerated back to the earth. At this tipping point (highest point), its vertical velocity will be zero, the gravitational force succeeded in stopping the ball in its track upwards.

This is no different if there is a horizonal component of the velocity. Gravity only affects the vertical component.