1. Free-fall: A ball is thrown vertically upward. What are its velocity and acceleration when it reaches its maximum altitude? What is its acceleration just before it hits the ground?

<A ball is thrown vertically upward. What are its velocity and acceleration when it reaches its maximum altitude?

At the maximum altitude the ball stops so what are its (instanteous) velocity and acceleration?

What is its acceleration just before it hits the ground? > What is the acceleration of any object falling under the force of gravity?

It's acceleration before it hits the ground will be equal to gravitational force

To determine the velocity and acceleration of a ball thrown vertically upward when it reaches its maximum altitude, we need to consider the forces acting on it.

1. Velocity at maximum altitude:
When the ball reaches its maximum altitude, its velocity becomes zero. This is because the ball momentarily comes to a stop before it starts descending due to the gravitational force acting on it.

2. Acceleration at maximum altitude:
At the maximum altitude, the ball experiences an acceleration due to gravity pulling it back downwards. The acceleration remains constant and is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 in the downward direction.

3. Acceleration just before hitting the ground:
As the ball descends towards the ground, the acceleration remains the same as before, which is approximately 9.8 m/s^2, directed downward. This is because the force of gravity continues to act on the ball, causing it to accelerate towards the ground.

So, in summary:
- When the ball reaches its maximum altitude, its velocity is zero.
- At the maximum altitude, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 downward.
- Just before hitting the ground, the acceleration remains the same, approximately 9.8 m/s^2 downward.

To answer these questions, we need to understand the concept of free-fall and the behavior of objects under the influence of gravity.

1. Velocity when the ball reaches maximum altitude:
When the ball is thrown vertically upward, its initial velocity is positive. As it rises, it decelerates due to the force of gravity. At the maximum altitude, the ball momentarily comes to a stop before it starts falling downward. At this point, its velocity becomes zero.

2. Acceleration when the ball reaches maximum altitude:
The acceleration of the ball remains constant throughout its motion, and it is equal to the acceleration due to gravity (g), which is approximately 9.8 m/s^2. At the maximum altitude, the ball experiences the same acceleration, but in the opposite direction, bringing its velocity to zero.

3. Acceleration just before the ball hits the ground:
Just before the ball hits the ground, its velocity is negative since it is moving downward. The acceleration remains the same, which is the acceleration due to gravity (-9.8 m/s^2). The negative sign indicates that the acceleration is in the opposite direction to the initial upward throw, as gravity pulls the ball downward.

To summarize:
- When the ball reaches its maximum altitude, its velocity is zero, and its acceleration remains the same as the acceleration due to gravity (-9.8 m/s^2) but in the opposite direction.
- Just before the ball hits the ground, its velocity is negative, and the acceleration remains the same (-9.8 m/s^2) in the downward direction.

Note: These explanations consider ideal conditions, neglecting air resistance.