It takes 5 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft?
Well, if the stone falls for 5 seconds, it sounds like the shaft is deep enough for the stone to have some serious second thoughts about its life choices.
To find the depth of the mine shaft, we can use the formula for the distance an object falls under the acceleration due to gravity:
d = (1/2) * g * t^2
Where:
d = depth of the mine shaft
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken for the stone to fall (5 seconds)
Plugging in the values, we have:
d = (1/2) * 9.8 m/s^2 * (5 s)^2
d = (1/2) * 9.8 m/s^2 * 25 s^2
d = 4.9 m/s^2 * 25 s^2
d = 122.5 meters
Therefore, the depth of the mine shaft is approximately 122.5 meters.
To determine the depth of the mine shaft, we can use the equation of motion for an object in free fall:
d = 0.5 * g * t^2
Where:
d = depth of the mine shaft
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
t = time taken for the stone to fall (5 seconds in this case)
Plug in the given values into the equation:
d = 0.5 * 9.8 * 5^2
d = 0.5 * 9.8 * 25
d = 122.5 meters
Therefore, the depth of the mine shaft is 122.5 meters.