You and your friend are leaning over the edge of the roof of a tall building. At the same instant you throw a baseball straight up with an initial speed vo and your friend throws a marble straight down with the same initial velocity vo. Assume that you can ignore air resistance. (1) Which object will reach the ground first, the baseball or the marble? (2) How will their speeds compare just before hitting the ground?

See my previous answer under "related questions" below

To determine which object will reach the ground first and how their speeds will compare, we need to analyze the motion of the baseball and the marble separately.

1) Which object will reach the ground first?
Since both objects have the same initial velocity and we are ignoring air resistance, both the baseball and the marble will experience the same acceleration due to gravity (approximately 9.8 m/s^2). In this case, the path of the marble is downwards, while the path of the baseball is upwards initially.

When an object is thrown vertically upwards, it reaches its maximum height first and then falls back down due to gravity. This means that the baseball will take longer to reach the ground compared to the marble.

Therefore, the marble will reach the ground first.

2) How will their speeds compare just before hitting the ground?
When both objects are close to the ground, their velocities will be nearly equal in magnitude but opposite in direction. This is because the gravity will have accelerated both objects to a similar speed.

In the case of the marble, its speed will continuously increase as it falls downward. Therefore, just before hitting the ground, the marble's speed will be equal to its initial speed vo, but in the opposite direction.

For the baseball, its speed will decrease on the way up due to the opposing force of gravity. At its highest point, the baseball will momentarily stop before starting to fall back down. As it falls, its speed will gradually increase, and just before hitting the ground, its speed will be equal to its initial speed vo.

So, in conclusion:
1) The marble will reach the ground first.
2) Just before hitting the ground, the marble's speed will be equal to its initial speed vo, but in the opposite direction. The baseball's speed will also be equal to its initial speed vo, but in the same direction as its initial motion.