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?
The object thrown downwards hits the ground first. That should be intuitively obvious.
They both hit the ground at the same speed, however. That follows from conservation of energy.
thank you
To determine which object will reach the ground first and how their speeds compare, we need to consider the motion of the objects separately.
For the baseball:
1. When you throw the baseball straight up, it will initially move upwards, slowed down by the force of gravity acting against it.
2. At a certain point, the baseball will reach its highest point (peak) and then start descending back towards the ground.
3. During its descent, the baseball will accelerate due to the force of gravity pulling it downwards.
4. When the baseball reaches the ground, its velocity will be negative, indicating that it is moving downwards.
For the marble:
1. When your friend throws the marble straight down, it will initially move downwards, accelerated by the force of gravity.
2. Throughout its motion, the marble will continue to accelerate due to the force of gravity acting in the same direction as its initial velocity.
3. When the marble reaches the ground, its velocity will be positive, indicating that it is moving downwards.
Now, let's answer the questions based on these observations:
1. Which object will reach the ground first?
The marble will reach the ground first. This is because it is already moving in the direction of gravity, while the baseball initially moves against gravity. The downward acceleration of the marble enables it to reach the ground faster than the baseball, which has to first slow down and then change its direction.
2. How will their speeds compare just before hitting the ground?
The magnitudes of their speeds just before hitting the ground will be the same. When both objects are about to hit the ground, their kinetic energies will be equal. This is due to the conservation of energy. However, their velocities will have opposite signs. The baseball will have a negative velocity since it is moving downwards, while the marble will have a positive velocity as it falls straight down.
In summary, the marble will reach the ground first, and just before hitting the ground, their speeds will have the same magnitude, but opposite signs.