When a ball is thrown upwards with some initial speed and then starts moving downward, its final velocity will depend on the initial velocity, the acceleration due to gravity, and the time it takes to change direction.
Let's assume the initial velocity of the ball when thrown upwards is denoted as u (positive value for upward direction), and the acceleration due to gravity is denoted as g (approximately 9.8 m/s², directed downward).
When the ball reaches its maximum height and starts moving downward, its velocity will be influenced by the acceleration due to gravity. The acceleration due to gravity is a constant value acting in the downward direction throughout the ball's trajectory.
To determine the final velocity, we need to know the time it takes for the ball to change direction. The time it takes to reach the highest point and come back down is twice the time it takes to reach the highest point alone.
Let's denote the time taken to reach the maximum height as t_up and the total time taken for the ball to return to its starting point as t_total.
At the highest point, the velocity will be momentarily zero. The time taken to reach the maximum height can be calculated using the equation:
u - g * t_up = 0 (initial velocity minus the deceleration due to gravity multiplied by the time taken)
Solving for t_up:
t_up = u / g
The total time taken for the ball to return to its starting point is given by:
t_total = 2 * t_up
Now, to calculate the final velocity, we need to determine the time it takes for the ball to fall from the maximum height to the starting point. This is half the total time taken (t_total / 2).
The final velocity, denoted as v_final, can be calculated using the equation:
v_final = u + g * t_down
where t_down is the time taken to fall from the maximum height to the starting point.
Since t_down = t_total / 2, we can substitute t_total / 2 for t_down:
v_final = u + g * (t_total / 2)
Substituting t_total = 2 * t_up:
v_final = u + g * (2 * t_up / 2)
Simplifying:
v_final = u + g * t_up
Therefore, the final velocity of the ball when it starts moving downward is equal to the initial velocity u. The acceleration due to gravity does not change the magnitude of the initial velocity, only its direction.