To determine the velocity of the stone when it is caught, we can use the concept of conservation of energy.
At the initial point when the stone is thrown upwards, it has potential energy and kinetic energy. As the stone reaches its maximum height, all of its initial kinetic energy is converted into potential energy. At the highest point, the stone's velocity is momentarily zero.
When the stone falls back down and is caught 5 meters above the ground, it has lost some potential energy and gained kinetic energy as it falls. The total mechanical energy (sum of potential energy and kinetic energy) of the stone is conserved throughout its motion.
Using the conservation of energy principle, we can equate the potential energy at the highest point to the sum of potential energy and kinetic energy when the stone is caught:
mgh = (1/2)mv^2
Where: m is the mass of the stone (we assume it cancels out), g is the acceleration due to gravity (approximately 9.8 m/s^2), h is the height difference between the highest point and the catching point (5 meters), and v is the velocity of the stone when it is caught.
Simplifying the equation, we have:
gh = (1/2)v^2
Solving for v, we get:
v = √(2gh)
Plugging in the values:
v = √(2 * 9.8 * 5)
Calculating the value:
v ≈ √98 ≈ 9.90 m/s
Therefore, when the stone is caught, its velocity is approximately 9.90 m/s downward.