When a ball is thrown vertically into the air, its velocity decreases until it reaches its highest point, also known as the peak of its trajectory. At this point, the ball momentarily stops moving upward and starts descending. The velocity becomes zero at the peak of the ball's trajectory.
The height at which the velocity becomes zero can be determined by using the equations of motion. In this case, we can use the equation for vertical motion under constant acceleration:
v² = u² + 2as
Where: v is the final velocity (which is zero at the peak), u is the initial velocity (the velocity with which the ball is thrown), a is the acceleration (which is equal to the acceleration due to gravity, approximately 9.8 m/s²), s is the displacement (the vertical height).
Since we are looking for the height at which the velocity becomes zero, we can rearrange the equation to solve for s:
0 = u² + 2as
From this equation, we can solve for s:
s = -u² / (2a)
It's important to note that the negative sign arises because we are considering the upward direction as positive and the downward direction as negative. The negative sign in the equation indicates that the height will be measured below the initial starting point.
Therefore, the height at which the velocity of the ball becomes zero is given by s = -u² / (2a).