To calculate the time taken for the electrician to fall from the 20th floor (100 meters above the ground) to the ground, we can use the basic physics equation for free fall under the influence of gravity, assuming air resistance is negligible.
The equation for the distance fallen under constant acceleration is given by:
\[ d = \frac{1}{2} g t^2 \]
Where:
- \( d \) is the distance (100 m)
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
- \( t \) is the time in seconds
Rearranging the equation to solve for \( t \):
\[ t^2 = \frac{2d}{g} \]
Substituting the known values:
\[ t^2 = \frac{2 \times 100 , \text{m}}{9.81 , \text{m/s}^2} \]
\[ t^2 = \frac{200}{9.81} \approx 20.387 , \text{s}^2 \]
Now, taking the square root:
\[ t \approx \sqrt{20.387} \approx 4.52 , \text{s} \]
Thus, the time taken for the electrician to fall from the 20th floor to the ground is approximately 4.52 seconds.