physic question

Question

A baseball player throws a ball with an initial velocity of 20m/s at 40º above horizontal. What is the ball's velocity when it is caught by his teammate across the field? Assume that the ball is thrown and caught at the same height.

Answer 1

The x-component (horizontal component) of the velocity remains constant, assuming there are no forces other than gravity (no air drag, for example).

The y-component (vertical component) varies but has a symmetry. For example, if the y-component when the ball is first thrown is 10 m/s, then (using g = 10 m/s^2 for simplicity instead of 9.8 m/s^2), one second later the y-component of velocity is 0 m/s (it is at the max height), and another second later, the it will be -10 m/s and back at the initial height. In general, the magnitude of the y-component will be the same at the same heights when going up and coming back down, but the sign flips.

So, the velocity when it returns to the original height will be 20 m/s but in the direction with 40 deg below the horizontal.