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On a pleasure cruise a boat is traveling relative to the water at a speed of 5.0 m/s due south. Relative to the boat, a passenger walks toward the back of the boat at a speed of 1.5 m/s. (a) What are the magnitude and direction of the passenger’s velocity relative to the water? (b) How long does it take for the passenger to walk a distance of 27 m on the boat? (c) How long does it take for the passenger to cover a distance of 27 m on the water?

(a) $v_{P W}=3.5 \mathrm{m} \cdot \mathrm{s}^{-1}$(b) $t=18 \mathrm{s}$(c) $t=7.71 \mathrm{s}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

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.

03:12

On a pleasure cruise a boa…

01:43

0:00

04:49

A boat can be rowed at 8.0…

05:08

Suppose that the ship in E…

02:03

(I) A person going for a m…

04:26

06:10

MMH A ferryboat is traveli…

01:52

A motorboat heads due east…

03:50

A river flows due south wi…

09:34

A boat moves through a riv…

so the question states that a boat travels at five meters per second due south relative to the water. So we're saying the origin is basically the water and is traveling at five meters per second. And we're also told that a person on the boat starts from the front of the boat and walks towards the back at 1.5 meters per second. So he's basically walking north and we're told that we need to find a couple of things. So the first thing we need to find is the magnitude of the velocity of the passenger relative to the water. So this is pretty easy to dio. We just need to find the length of the vector that connects the origin. So I'm just gonna read it off to the side on in reality would be on top of this vector in the middle, but so we need to find the the length of the vector that connects the origin to the tip of the vector of the passenger walking back towards the front. And so to do this, we can just subtract the vector that's moving at five meters per second from the 1.5 meters per second vector and that gives us a, uh speed of the passenger relative to the water. So but when we do this, we get 3.5 meters per second in the south direction. And this makes sense because you know that the boat is moving down at five meters per second and the person is counter acting this motion by moving back up at 1.5 meters per second. So 3.5 meters per second does make sense in this out direction. So now we're asked, How long does it take for the man to G O 27 meters on the boat? So we know that on the boot he's moving 1.5 meters per second so we can just use our kingdom attics equations with state that the initial velocity times a time is equal to change in displacement. And we know that his velocity is 1.5 meters per second. We're trying to find the time and we know his displacement is 27 meters. So the time it takes him to go 27 meters on the boat is 18 seconds. Now, if we're trying to find the time it takes for him to move 27 meters on the water. We have to use this vector, um that we calculated to be 3.5 meters per second. So we just do do the same thing that we did appear. So we're saying 3.5 meters per second is his speed. We don't know the time it takes and we know the distance is 27 meters, so we can divide by 3.5 almost sides and we get that the time is equal to 7.71 seconds, and that's the answer.

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