Question

If we are running on a threadmill with a speed such that I appear stationary and throw a ball, will the ball go further as compared to one who throws the ball while he is standing stationary.

The concern is that though I appear stationary while I am running on a threadmill, I do have a certain speed. Therefore the ball would have some initial horizontal speed.

Answer 1

In laboratory (earth-fixed) coordinates, you are stationary. The motion of the treadmill will not help the ball go farther.

It you throw while failing to run on a movind treadmill (before falling off), you will be moving backwards in lab coordinates, and the ball will go less far.