To determine the velocity of the object just before it hits the floor after falling from a height of 3 meters, we can use the principle of conservation of energy or kinematic equations. Here, we'll use the kinematic equations.
The object starts from rest when it falls, so its initial velocity (u) is 0 m/s. The distance (s) it falls is 3 meters, and we can use the acceleration due to gravity (g), which is approximately \(9.81 , \text{m/s}^2\).
Using the following kinematic equation:
\[ v^2 = u^2 + 2as \]
where:
- \(v\) = final velocity (the value we want to find),
- \(u\) = initial velocity (0 m/s),
- \(a\) = acceleration (gravity, \(9.81 , \text{m/s}^2\)),
- \(s\) = distance fallen (3 m).
Substituting in the known values:
\[ v^2 = 0^2 + 2 \times 9.81 , \text{m/s}^2 \times 3 , \text{m} \] \[ v^2 = 0 + 58.86 \] \[ v^2 = 58.86 \] \[ v = \sqrt{58.86} \approx 7.67 , \text{m/s} \]
Thus, the velocity of the object when it hits the floor is approximately 7.67 m/s.
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