The Physics
* Free Fall: When an object falls freely, its acceleration is due to gravity (approximately 9.8 m/s²). This means its velocity increases by 9.8 meters per second every second.
* Distance Formula: The distance an object falls is directly proportional to the square of the time it falls. The formula is:
* Distance (d) = (1/2) * g * t²
* Where:
* d = distance
* g = acceleration due to gravity
* t = time
Doubling the Time
Let's say the object falls for a time 't'. Now, we double the time to '2t'. Plugging this into the formula:
* Distance (d') = (1/2) * g * (2t)²
* d' = (1/2) * g * 4t²
* d' = 4 * (1/2) * g * t²
Notice that d' = 4 * d. This means the distance traveled when the time is doubled is four times the original distance.
In Summary
Doubling the falling time under constant gravity doesn't just double the distance, it quadruples it because of the squared relationship between distance and time in the free fall equation.
