00:01
Hi there, so for this problem we have the situation that is shown in here.
00:05
We are told that a boat is pulled into a dock by being set for a rope.
00:09
This is shown in this figure.
00:10
Now the rope is attached to the bow of the boat at a point that is 11 feet below the pulley.
00:17
So this distance in here, let me just draw a triangle.
00:26
Well, let me just do it with the ruler.
00:31
Okay, so this distance that we are here.
00:38
Given in here, this distance is 10.
00:42
And if the rope is pulled through the pulley at a rate of 20 feet per minute, so let's call this the length l of the rope.
00:59
So we are told that it is being pulled.
01:05
So that means that the rate of change of l is the the distance l is decreasing, so that will be minus the value that we are given, which is 20 feet per minute.
01:21
And the question is, at what rate will the boat be approaching? so let's call the distance of the both to the to the dock as ads.
01:36
So what we need to determine is the rate of change of ads with respect to time.
01:41
This, when 100 feet of rope is out, so that means when the value of l, which is the length of the row, is 100.
01:57
Then for this, we need to use trigonometry.
02:00
For this, we can use the pythagorean theorem.
02:03
We know that l squared, which is the hypotenus in this case, is equal to x squared plus, 10 to the square.
02:14
So that will be x squared plus 100.
02:18
Then we can derive both sides of this with respect to time...