1. Initial Conditions:
* Same Velocity: Both stones start with the same upward velocity.
* Different Masses: One stone is heavier (has more mass) than the other.
2. Ascent:
* Equal Initial Kinetic Energy: Since they have the same initial velocity, they both have the same initial kinetic energy (KE = 1/2 * mv^2, where m is mass and v is velocity).
* Work Done by Gravity: Gravity does negative work on both stones, slowing them down as they ascend.
* Height Reached: The stone with the lesser mass will reach a slightly higher height. This is because the lighter stone has a lower gravitational force acting on it, meaning it loses less kinetic energy to gravity during its ascent.
3. Descent:
* Acceleration Due to Gravity: Both stones experience the same acceleration due to gravity (g = 9.8 m/s²) during their descent.
* Time of Fall: The stone with the lesser mass will take slightly longer to fall back to the ground. This is because the lighter stone experiences less gravitational force and thus accelerates at a slightly slower rate.
* Impact Velocity: Both stones will hit the ground with the same final velocity. This is because they started with the same initial velocity, and gravity's acceleration acts equally on both, regardless of mass.
In Summary:
* The lighter stone will go slightly higher than the heavier stone.
* The lighter stone will take a slightly longer time to fall back to the ground.
* Both stones will hit the ground with the same final velocity.
Important Note: Air resistance can play a role, especially if the stones are significantly different in shape or size. Air resistance will generally cause the heavier stone to fall slightly faster, as it's less affected by air drag.
