Continue walking at a constant speed. Just after you release the ball upward, break into a run. Where does the ball land?
To determine where the ball lands, we need to consider the horizontal and vertical motion of the ball separately.
First, let's examine the horizontal motion. Since you continue walking at a constant speed, your horizontal motion is unaffected. As a result, the ball will also continue to move horizontally at a constant velocity. Therefore, the position of the ball in the horizontal direction remains unchanged throughout its flight.
Now, let's focus on the vertical motion of the ball. When you release the ball upward, it experiences an initial upward velocity. However, gravity acts to slow down its upward motion until it reaches its peak height. At that point, the ball starts to fall downward due to gravity.
When you break into a run just after releasing the ball, your horizontal motion becomes faster, but it doesn't impact the vertical motion of the ball. The ball will continue to follow its initial vertical motion regardless of your speed.
Assuming there are no other external factors like air resistance, if the ball was released at a height above the ground and we neglect any additional forces acting on it, the ball will follow a parabolic trajectory. It will reach its peak height and then fall back down to the ground.
Therefore, no matter how fast you start running, the ball will land at the same spot as if you had not started running at all. The only factors that affect where the ball lands are the initial velocity of the ball when you release it, the angle at which it is released, and the height from which it is released.