00:01
So we have a boat, and we'll say that this is the tip of the boat, and it's approaching a dock, and we have a pulley that is mounted five feet above, and we can put that as a constant because it is something that is not changing.
00:16
And we have the pulley up here, and we know that the boat has the rope attached to that pulley system, and let me try to draw that diagonal up there.
00:26
And let's call this distance x that the boat is, so where the boat is here, and we'll just say it's like a sailboat.
00:34
And it is being pulled this way.
00:36
So x is getting smaller.
00:39
And again, we can label that as a constant because this pulley is always staying five feet above that dock.
00:47
And so this dimension is changing.
00:50
I'll call this z.
00:52
And we are given that this is getting, whoops, we're change that to a z.
00:58
We are having the rope pulled and it is pulling in at 20 feet per second.
01:07
I'm sorry, 20 feet per minute.
01:10
That's how much it's moving.
01:11
That'd be extremely fast for doing it per second.
01:14
And z is getting smaller because it's being pulled in.
01:17
So we would consider that to be a negative rate.
01:20
So that's what we're given.
01:22
We're given this picture and we're given that rate.
01:24
And what do we want to find? we want to find in another picture.
01:28
I always tell my students when we're doing these related rate problems, write one of them that has all the things that vary down.
01:36
If it's a constant, put it.
01:38
And then we specifically want to find when this distance out is 110 feet, this is 5 feet.
01:49
We want to know what dx, dt is the moment that z is 110 feet out.
01:56
And so we could use pythagorean theorem to figure out what this value is for this...