Raindrops fall 1060 m from a cloud to the ground. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground?
Well, if raindrops weren't slowed down by air resistance, they would definitely have some serious need for a parachute! But let's entertain ourselves with the idea. Considering there are no external forces slowing them down, the raindrops would be accelerating due to gravity. Using the equation of motion, we can calculate their final velocity. So, after falling from 1060 m, the raindrops would be moving at a hilarious speed, approximately equal to "Oh my goodness, put on your running shoes!" meters per second. But don't worry, in reality, the air resistance would make their descent a bit more modest!
To calculate the final velocity of the raindrops when they strike the ground, we can use the equation for free fall:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity (which is 0, because the raindrops start at rest)
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = displacement or height (1060 m, the distance the raindrops fall)
Plugging in the values, we can solve for v:
v^2 = 0^2 + 2 * 9.8 m/s^2 * 1060 m
v^2 = 2 * 9.8 m/s^2 * 1060 m
v^2 = 2060 m^2/s^2
v = √(2060 m^2/s^2)
v ≈ 45.43 m/s
Therefore, if the raindrops were not slowed by air resistance, they would be moving at approximately 45.43 m/s when they strike the ground.
To calculate the speed at which the raindrops would be moving when they strike the ground, we can use the principles of kinematics and the equation for free fall motion.
The equation for free fall motion without air resistance is:
v = sqrt(2gh)
Where:
v is the final velocity of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
h is the height or distance the object falls
In this case, the height or distance the raindrops fall is given as 1060 m.
Substituting the known values into the equation:
v = sqrt(2 * 9.8 m/s^2 * 1060 m)
v = sqrt(20596 m^2/s^2)
v ≈ 143.54 m/s
Therefore, if the raindrops were not slowed by air resistance, they would be moving at a speed of approximately 143.54 m/s when they strike the ground.