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MMH A ferryboat is traveling in a direction 38.0 north of east with a speed of 5.50 m/s relative to the water. A passenger is walking with a velocity of 2.50 m/s due east relative to the boat. What is the velocity (magnitude and direction) of the passenger with respect to the water? Determine the directional angle relative to due east.

$v_{P W}=7.63 \mathrm{m} \cdot \mathrm{s}^{-1}$$\theta_{1}=26.36^{\circ}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

04:19

MMH A ferryboat is traveli…

05:59

As an aid in working this …

06:57

. As an aid in working thi…

A ferryboat is traveling i…

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06:31

$\because$ A passenger wal…

07:11

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01:14

A ship sets sail from Rott…

14:07

A Coast Guard ship is tra…

05:00

As two boats approach the …

04:32

A boat can travel 2.20 m/s…

So the question states that a boat moving at a 38 degree angle from due east at 5.5 meters per second, she's a person walking due east at 2.5 meters per second. Uh, relative to the bow and we're trying to find the angle as well as the magnitude of the velocity of the person relative to the water. So to solve this problem, we should first draw a diagram of what it would look like so relative to the water. So we're going to say this year is like the origin of the water so relative to the water, the vector that describes the boat would look something like this where this angle here is 38 degrees and it's moving at 5.5 meters per second. So now that we have this vector that describes the boat, we can draw in the vector that describes the person relative to what is viewed from the boat. So say that boat is here relative Teoh. To this point, the vector of the person appears to be moving like this, due east at 2.5 meters per second, and we're trying to find the vector that comes from the origin and reaches the person who's at this point here. So this vector here will call it the capital. V describes the motion of the person relative to the water. So to find this we can see here is just some simple vector geometry where we have to add the victor from, uh, the boat relative to the water and add it to the vector of the person relative to the boat. And that'll give us this vector with Capital V. So let's write out the vector components first to make it a little bit easier. So the vectors that described the boat relative to the water are so so it's going to be in the horizontal direction. It's going to be 5.5 times co sign of 38 degrees, right, because co sign of 38 degrees is adjacent. Overhype on use and are adjacent is our, um, corazon, a component of the velocity so we can just sell for that and we get this for 5.5 coastline of 38 degrees and are vertical component is going to be pretty much the same thing. But instead of co sign sign of 38 degrees. And then for the vector that describes the person walking relative to the boat, they're horizontal. Component is just going to be 2.5 and they don't have any sort of vertical component. So it's pretty easy to add these vectors. Um, you're just gonna get so we're adding these. You just gonna get 5.5 co sign 38 degrees plus 2.5 and 5.5 sign 38 degrees. And this is going to be your vector. So to find the magnitude of this vector, we're just gonna take the square root of the X component squared, plus the Y component square said the X component squared is going to be 5.5 co sign 38 degrees close to point foot. Sorry, that's not supposed to be a point. There. Two point five squared plus, um, 5.5 sign of 38 degrees square. And when we do this, we end up getting a value of 7.63 meters per second for the, uh, person. So now that we know that we know that this is our capital V, we can find the angle it makes with, uh, due East. So probably the easiest way to do this is look at the components again. So we know that the hypothesis of this vector is 7.63 And we know that the vertical component of this vector, as we see appear, is 5.5 times sign of 38 degrees. All right, because this is the only contribution of the vertical component is due to this specter. So Ah, what we can do is we can just take thes sine inverse, which is going to be opposite over high Polynesians. Took the opposite in this case is just this vertical component vectors 5.5 times signed 30 degrees overhype on us, which is 7.63 meters per second. And when we do this, we find that the angle is equal to 26.35 degrees. That's the answer

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