To calculate the time it takes for a mango to fall from a height of 5 meters, we can use the formula derived from the laws of physics for free fall under the influence of gravity:
\[ d = \frac{1}{2} g t^2 \]
Where:
- \( d \) is the distance fallen (5 meters in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( t \) is the time in seconds.
Rearranging the formula to solve for \( t \):
\[ t^2 = \frac{2d}{g} \] \[ t = \sqrt{\frac{2d}{g}} \]
Substituting in the values:
\[ t = \sqrt{\frac{2 \times 5 , \text{m}}{9.81 , \text{m/s}^2}} \] \[ t = \sqrt{\frac{10}{9.81}} \approx \sqrt{1.019} \approx 1.01 , \text{s} \]
So, it takes approximately 1.01 seconds for the mango to reach the ground.