To determine the velocity of the stone when it is at a height of 5m above the ground, we can use the laws of motion and the principle of conservation of energy.
When the stone is dropped from a rest position 10m above the ground, it will undergo free fall. The acceleration due to gravity (g) acts in the downward direction and remains constant throughout the motion.
Let's denote:
- Initial height (h_initial) = 10m
- Final height (h_final) = 5m
- Initial velocity (u) = 0 (stone is dropped from rest)
- Final velocity (v) = ?
Using the principle of conservation of energy, we can equate the potential energy at the initial height to the sum of the potential energy at the final height and the kinetic energy of the stone:
mgh_initial = mgh_final + (1/2)mv²
Here, m represents the mass of the stone, g is the acceleration due to gravity, and v is the final velocity.
Since the mass of the stone appears on both sides of the equation and cancels out, we can simplify the equation to:
gh_initial = gh_final + (1/2)v²
Substituting the given values:
(9.8 m/s²)(10m) = (9.8 m/s²)(5m) + (1/2)v²
98 m²/s² = 49 m²/s² + (1/2)v²
49 m²/s² = (1/2)v²
Simplifying further:
98 m²/s² = v²
Taking the square root of both sides:
v = √98 m/s
v ≈ 9.9 m/s
Therefore, the velocity of the stone when it is at a height of 5m above the ground is approximately 9.9 m/s.