A canoe can travel at a maximum speed of 2.5 m/s relative to...

A canoe can travel at a maximum speed of 2.5 m/s relative to the water. The canoe is traveling on a river whose current travels at 3.2 m/s relative to the shore. a) What is the velocity of the canoer relative to the shore if they are paddling as hard as they can down stream (in the direction the water flows)? b) What is the velocity of the canoer relative to the shore if they are paddle as hard as they can up stream (against the flow of the water)? c) The canoer gives decides they've had enough for one day, so they point their canoe straight at the shore and paddle as hard as they can. What is their velocity relative to the shore? Hint: How the person paddles is what determines their velocity relative to the water.

Transcript

00:01 In this problem, you have relative motion.

00:04 You're trying to have velocities relative to one quantity, and you need it relative to a different quantity.

00:13 So these are relative motion problems.

00:17 And an example, close to what you're going to be dealing with in this problem, is the following.

00:24 Say you have a boat, and that's related to the shore.

00:29 And you've got a person moving on that boat, and you want the person relative to the shore, motion relative to the shore.

00:36 How do you do it? well, you add up the motion of the person on the boat.

00:42 That's relative to the boat.

00:44 Plus, what the boat is doing relative to the shore.

00:47 You add those two as vectors, as vectors, and you get what the person is doing relative to the shore, the motion of the person relative to the shore.

00:55 That's how it works.

00:56 So it really is a vector addition problem, these relative motion problems.

01:04 So in this case, we have a canoe that relative to the water.

01:08 This is what the notation is.

01:09 Canoe relative to the water, water relative to the shore.

01:13 So we have a speed of the canoe, maximum speed technically, and that's what it will be throughout the problem, three problems, three parts, of 2 .5 minutes per second.

01:24 And the water relative to the shore is 3 .2 meters per cent.

01:29 That's current.

01:31 Now, the first case is we have, let's just say, water is moving to the right.

01:38 That's our downstream.

01:44 So that's the water relative to the shore.

01:47 We also have the canoe paddling in the same direction.

01:57 So those are two vectors.

01:59 And we'll make, in all three parts, i'll make my axes traditional set.

02:07 Now, as i was mentioning, just a minute ago with that boat in person example, the canoe route to the shore will be the canoe relative to the water plus the water relative to the shore.

02:23 But again, as vectors, not as numbers, but as vectors.

02:30 Now, let's look at this graphically.

02:32 I've already kind of set it up.

02:35 Remember the triangle rule, tail of the second vector puts at the tip of the first, and you draw from the tail of the first to the tip of the second.

02:45 This is vcs, the canoe relative to the shore.

02:51 It's a vector addition.

02:52 I use the triangle rule.

02:56 Now, let's look, it's only x component here.

03:02 So let's look at the x components.

03:05 So it's just going to be the sum of the x components, which in this case are both in the positive, both vectors are in the positive x direction.

03:14 So this is plus 2 .5 meters per second, plus 3 .2.

03:20 Actually, let me add one extra step in there so you see it.

03:25 So this will be vcw plus vws.

03:30 Because those are the magnitudes, but when you're one -dimensional, you either put a plus on it when the vector is in the positive direction or minus -nine when it's in the negative direction.

03:39 So they're both in the positive direction.

03:41 So then this is 2 .5 meters per second plus 3 .2 meters per second, 5 .7 meters per second.

03:53 So relative to someone on the shore, that's what the person on the shore says that the canoe is actually traveling, 5 .7 meters per second.

04:03 To them.

04:05 It's all matter of what frame of reference you're talking about.

04:10 To the shore.

04:10 That's what it says.

04:14 Now, one other thing before i go on to the next part, notice something i've done that is very useful.

04:21 You're looking for the canoe route to the shore.

04:24 Notice on the right -hand side, the ws are side by side.

04:29 You can think when they're side by side of them being eliminated, and you have c -s left over.

04:37 So that's how you can tell that you've got the right vector summation by being able to eliminate the middle symbol and just that the two ends are the same as what you have on the left.

04:51 So if you had cw and sw, that's wrong.

04:57 It does not give me this.

05:01 So it's a way of checking, checking yourself.

05:04 It's a very nice way of knowing what you gotta add together as vectors.

05:09 So that was part, part b.

05:14 Now you still have the, still have the, nothing ever changes with the current, the flow of the water...

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