If raindrops fell with no air drag how long would it take?

In summary, the student attempted to solve the problem of calculating the speed of drops falling from a cloud 1.6 kilometers above the Earth's surface with no air drag. They used the equation d = 0.5gt^2 + v_0*t and substituted in the given values, resulting in a final answer of t = 326 seconds. However, they realized that they forgot to take the square root of 1600 and that the correct answer should be sqrt(326).
  • #1
iluvpandas
7
0

Homework Statement



If there were no air drag, how fast would drops fall from a cloud 1.6 kilometer above the Earth's surface?

Homework Equations


am i heading in the right direction if not what am i doing wrong?


The Attempt at a Solution



i tried converting to m first then i divided both by 2 getting

2d=at^2 and then i divided both by the acceleration which i assumed to be gravity (9.8) after that i had 2(1600)/9.8=t^2 and to get rid of the exponet i rooted both sides and got 326.5
 
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  • #2
Yes,

d = 0.5gt^2 + v_0*t
v_0 = 0
1.6km = 0.5*9.81*t^2
t = 326..
 
  • #3
when i ented the answer the web assignment said it was wrong though and now I am kind of confused as to what i did wrong.
 
  • #4
iluvpandas said:
when i ented the answer the web assignment said it was wrong though and now I am kind of confused as to what i did wrong.

Because it is sqrt(326). I just recognized that. I also forgot to take square root
 

1. How does air drag affect the falling speed of raindrops?

Air drag, also known as air resistance, is a force that opposes the motion of an object through the air. It is caused by the collision of air molecules with the surface of the object. In the case of raindrops, air drag slows down their falling speed, making them fall slower than they would in a vacuum.

2. What would be the falling speed of raindrops without air drag?

Without air drag, raindrops would accelerate at a rate of 9.8 meters per second squared (m/s²) due to the force of gravity. However, their maximum speed would depend on their size and shape. Smaller raindrops would fall faster than larger ones.

3. How long would it take for raindrops to reach the ground with no air drag?

The time it takes for a raindrop to fall with no air drag can be calculated using the equation t = √(2h/g), where t is time, h is the initial height, and g is the acceleration due to gravity. For example, a raindrop starting at a height of 1000 meters would take approximately 14.3 seconds to reach the ground.

4. Would raindrops fall at the same speed regardless of their size?

No, the size and shape of a raindrop can affect its falling speed even without air drag. Smaller raindrops have a higher surface area to volume ratio, which means they experience less air resistance and can fall faster than larger raindrops of the same shape.

5. What other factors besides air drag can affect the falling speed of raindrops?

In addition to air drag, the density and viscosity of the air, as well as the temperature and humidity, can also affect the falling speed of raindrops. These factors can change the air resistance and the rate at which the raindrops evaporate, altering their size and shape and ultimately affecting their falling speed.

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