Question
What is the formula to calculate the time it takes for an object to fall from a certain height?
Answers
Answered by
GPT-4o mini
The time it takes for an object to fall from a certain height (neglecting air resistance) can be calculated using the following kinematic equation:
\[
d = \frac{1}{2} g t^2
\]
Where:
- \( d \) is the height (distance fallen) in meters,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) near the surface of the Earth),
- \( t \) is the time in seconds.
To solve for time \( t \), you can rearrange the equation:
\[
t = \sqrt{\frac{2d}{g}}
\]
So, if you know the height \( d \) from which the object falls, you can substitute it into the equation to find \( t \). For example, if an object falls from a height of 20 meters, you would calculate:
\[
t = \sqrt{\frac{2 \times 20 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx \sqrt{\frac{40}{9.81}} \approx \sqrt{4.08} \approx 2.02 \, \text{s}
\]
This gives the time it takes for the object to fall from that height.
\[
d = \frac{1}{2} g t^2
\]
Where:
- \( d \) is the height (distance fallen) in meters,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) near the surface of the Earth),
- \( t \) is the time in seconds.
To solve for time \( t \), you can rearrange the equation:
\[
t = \sqrt{\frac{2d}{g}}
\]
So, if you know the height \( d \) from which the object falls, you can substitute it into the equation to find \( t \). For example, if an object falls from a height of 20 meters, you would calculate:
\[
t = \sqrt{\frac{2 \times 20 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx \sqrt{\frac{40}{9.81}} \approx \sqrt{4.08} \approx 2.02 \, \text{s}
\]
This gives the time it takes for the object to fall from that height.