The captain of a boat wants to travel directly across a...

The captain of a boat wants to travel directly across a river that flows due east with a speed of $1.00 \mathrm{~m} / \mathrm{s} .$ He starts from the south bank of the river and heads toward the north bank. The boat has a speed of $6.10 \mathrm{~m} / \mathrm{s}$ with respect to the water. In what direction (in degrees) should the captain steer the boat? Note that $90^{\circ}$ is east, $180^{\circ}$ is south, $270^{\circ}$ is west, and $360^{\circ}$ is north.

Transcript

00:01 So in this problem, we have carnal directions.

00:03 So first thing we should do is label how that works on our paper.

00:06 Conventionally, north, south, up and down, west and east, left and right.

00:14 We're also told the angles for the directions in this problem.

00:18 East is going to be 90 degrees, south, 180 degrees.

00:22 West is 270 degrees.

00:24 North is 360 degrees.

00:30 Part of screen doesn't work very well.

00:31 And also zero if we go the other way from 90.

00:36 So we have that, and we're told that the river flows due east.

00:43 And the river flow is going to be parallel to the river.

00:45 So if the river is flowing east, then that means the river banks are going to be horizontal on a paper with our axis.

00:54 So what the captain wants to do is cross straight across the river.

00:58 And that means the velocity of the boat relative to the earth, is going to have to be strictly north, considering that our river is east.

01:09 And it's important that we specify that this is the velocity of the boat relative to the earth, and that's how we write that.

01:14 We can also put a slash in.

01:17 So we also know that the river is flowing.

01:21 We know the river is flowing east, so we can draw it in the east direction.

01:25 And this is the velocity of the water relative to the earth, and that's equal to one meter per second.

01:36 So the boat can travel some direction, but we want to see because it could be any way.

01:43 And the resulting velocity of the boat compared to the earth should be horizontal.

01:51 But we see that the boat's in the water, and so the water is going to kind of push it over.

01:56 So the boat needs to counteract.

01:59 So let's set up that our velocity of the boat goes from the velocity of the water to the tip of the velocity of the boat relative to the earth.

02:07 So the velocity vector we just drawn is the velocity of the boat relative to the water.

02:14 Now this is 6 .1 meters per second by the problem.

02:18 And i would pick our angle here to be angle theta.

02:22 So what we set up here is a relative motion problem, and boat in the river is a good key to see relative motion.

02:30 Now we see we have a vector addition.

02:32 This is what we don't know.

02:33 We have two vectors that we do...

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