How long would it take for a small pebble to fall from the top of the Grand Canyon to its deepest part?
To determine how long it would take for a small pebble to fall from the top of the Grand Canyon to its deepest part, we can use the laws of physics.
Let's make some assumptions to simplify the calculation:
1. Consider the Grand Canyon as a straight vertical drop.
2. Ignore any air resistance.
3. Assume the small pebble falls freely without any initial velocity.
The time it takes for an object to fall freely can be calculated using the equation:
t = √(2h/g),
where:
t is the time it takes to fall,
h is the vertical distance, and
g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
To find the vertical distance, we need to know the height and depth of the Grand Canyon.
The average depth of the Grand Canyon is approximately 1,600 meters, while the highest point is about 2,450 meters above sea level. Therefore, the total vertical distance the pebble would fall is 4,050 meters.
Plugging these values into the equation, we get:
t = √(2 * 4050 / 9.8) = √828.57
Simplifying further, we find:
t ≈ 28.78 seconds
So, it would take approximately 28.78 seconds for a small pebble to fall from the top of the Grand Canyon to its deepest part, assuming the mentioned assumptions hold true.
To calculate the time it would take for a small pebble to fall from the top of the Grand Canyon to its deepest part, we can use the laws of physics. The time it takes for an object to fall freely from a certain height can be determined using the equation:
Time = Square root((2 * height) / g)
Where:
- Time is the time it takes for the object to fall
- Height is the vertical distance the object falls
- g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth
First, we need to find the height difference between the top and the deepest part of the Grand Canyon. The elevation of the Grand Canyon South Rim is approximately 2,134 meters (7,001 feet), and the elevation of the lowest point, at the Colorado River, is approximately 735 meters (2,415 feet).
Height = 2,134 m - 735 m = 1,399 meters
Now we can calculate the time it would take for the pebble to fall:
Time = Square root((2 * 1,399 m) / 9.8 m/s^2)
Using a calculator, we can find that the time is approximately 16.6 seconds.
Therefore, it would take around 16.6 seconds for a small pebble to fall from the top to the deepest part of the Grand Canyon.