00:01
Hi there, so for this problem we have a rain drop with a radius capital art equals to 1 .5 millimeters and falls from a cloud that is at a height age equal to 1 ,200 meters about the round.
00:29
So the drag coefficient c is also given, and that value is 0 .6.
00:39
And we need to assume that the drop is spherical and throughout its fall.
00:46
So the density of water, we are also given density of water, and that is equal to 1 ,000 kilograms per cubic meter, and the density of earth is also given.
01:02
Density of earth.
01:05
This is the density of water and this is the density of earth, which is equal to 1 .2 kilograms per cubic meter.
01:17
So the question for this is what is the terminal speed? so to calculate that, we use the following equation.
01:33
We note that in this case the terminal velocity is when the force due to gravity is balanced by the draft force.
01:40
The object will no longer speed up or slow down, but will continue falling at a constant velocity that is called the terminal velocity.
01:52
And the terminal velocity is going to be equal to the square root of two times the mass times acceleration due to gravity.
02:10
As you can see from here, this corresponds to two times the weight of the temperature, drop of water and this over the density of the median, which in this case is the density of earth, and this times the area and times the coefficient of drag, that we call it just simply by c.
02:35
Now the first thing that we need to determine is the mass.
02:40
And the mass can be obtained from the equation of the density of water that we know is the mass over the volume.
02:51
Now, if we solve for the mass, we will obtain that that is the product between the density of water times the volume of this drop of water.
03:01
So, we have the density of water times four over three times pi times the radius of the drain drop to the cube.
03:15
So we just need to simply substitute those values in here to obtain the mass.
03:25
So we have this, we have 4 over 3 times pi times the radius.
03:32
And the radius that is given for this drop is 1 .5 millimeters.
03:38
We know that millie means 10 to the minus 3...