How to find velocity of a falling object given mass and distance?
The Correct Answer and Explanation is:
To find the velocity of a falling object when given its mass and distance, we can use a formula from physics that relates distance fallen under constant acceleration due to gravity:
Formula (ignoring air resistance):
v=2gdv = \sqrt{2gd}v=2gd
Where:
- vvv is the final velocity (in meters per second)
- ggg is the acceleration due to gravity (approximately 9.8 m/s29.8 \, \text{m/s}^29.8m/s2 on Earth)
- ddd is the vertical distance the object falls (in meters)
Important Note:
Mass is not needed to find the velocity in this context. This is because all objects fall at the same rate in a vacuum regardless of mass, due to the universality of free fall under gravity.
Example Calculation:
Suppose an object falls a distance of 20 meters. The velocity just before impact is:v=2×9.8×20=392≈19.8 m/sv = \sqrt{2 \times 9.8 \times 20} = \sqrt{392} \approx 19.8 \, \text{m/s}v=2×9.8×20=392≈19.8m/s
Explanation
In physics, when an object is dropped from a certain height and falls freely under the influence of gravity, its velocity increases over time. The force of gravity pulls it downward, causing it to accelerate at a constant rate. On Earth, this acceleration is approximately 9.8 m/s29.8 \, \text{m/s}^29.8m/s2. The object’s mass does not affect how fast it falls because gravity accelerates all objects equally when air resistance is ignored. This principle was famously demonstrated by Galileo.
To find the velocity of a falling object just before it hits the ground, you can use the equation derived from the laws of motion. This equation assumes the object starts from rest (initial velocity is zero) and accelerates uniformly due to gravity. The formula is v=2gdv = \sqrt{2gd}v=2gd, where ggg is the acceleration due to gravity and ddd is the distance fallen.
This formula comes from combining two kinematic equations. One equation states that the final velocity squared equals the initial velocity squared plus two times acceleration times distance. Since the object is falling from rest, the initial velocity is zero, and the equation simplifies to v=2gdv = \sqrt{2gd}v=2gd.
Therefore, by knowing the distance the object has fallen, you can accurately determine its final velocity without needing its mass. This formula is useful in basic physics, especially when analyzing free fall motion in ideal conditions.
