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.
V^2/2 = g H
(from conservation of energy)
V = sqrt(2 g H)
H = 2400 m
g = 9.8 m/s^2
Solve for V
47040
To determine the speed at which the drops would fall without air drag, we can use the equation of motion. The equation for the speed of an object in free fall is given by:
v = sqrt(2gh)
Where:
v is the final velocity (speed) of the object,
g is the acceleration due to gravity (approximately 9.8 m/s²), and
h is the height or distance the object falls.
In this case, the height or distance is 2.4 kilometers, which we need to convert to meters. Since 1 kilometer is equal to 1000 meters, the height in meters would be 2400 meters.
Plugging in the values into the equation, we have:
v = sqrt(2 * 9.8 * 2400)
v = sqrt(47040)
Using a calculator, we find that sqrt(47040) is approximately 216.84 m/s.
Therefore, without air drag, the drops would fall at a speed of approximately 216.84 m/s from a cloud 2.4 kilometers above the Earth's surface.