If there were no air drag, how fast would drops fall from a cloud 2.4 kilometer above the Earth's surface?
Answer in m/s.
vf^2=2gh
Vf= sqrt (2*g*h)
To calculate the speed at which drops would fall from a height of 2.4 kilometers above the Earth's surface without considering air drag, we can use the equation for free fall.
The formula for free fall is:
v = √(2gh)
where:
v = final velocity (the speed of the drop when it reaches the ground)
g = acceleration due to gravity (approximately 9.8 m/s² on Earth)
h = height or distance fallen
Given that the height is 2.4 kilometers, we need to convert it to meters before substituting it into the equation. There are 1,000 meters in 1 kilometer, so:
Height = 2.4 kilometers × 1,000 meters/kilometer = 2,400 meters
Now, let's substitute the values into the equation:
v = √(2 × 9.8 m/s² × 2,400 m)
After evaluating the expression inside the square root:
v = √(47,040 m²/s²)
Finally, taking the square root:
v ≈ 217 m/s
Therefore, if there were no air drag, the drops would fall at a speed of approximately 217 meters per second (m/s) from a cloud 2.4 kilometers above the Earth's surface.