A ball is thrown into the air at some angle. At the very top of the ball's path, what is always 0?

1 Answer
Oct 29, 2015

The vertical component of the velocity.


If the initial vertical velocity were defined as positive at 10 m/s, then we can calculate what the vertical velocity will be at all other times. As long as the velocity is positive, the ball will be moving upward. When the velocity becomes negative, the ball will be moving downward. The top of the arc is the point where it stops moving up and starts moving down.

Something initially moving upward and later moving downward must, at some time in between have a zero vertical velocity. The notion that a continuous function will, at some time, pass through all values in between some past value and a later value is actually a statement of the fundamental theorem of calculus.

The acceleration is constant. The velocity is constantly changing. But, at some time, the velocity will be zero.