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SSM Mario, a hockey player, is skating due south at a speed of 7.0 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 11.0 m/s and is moving in a direction of 22 west of south, relative to the ice. What are the magnitude and direction (relative to due south) of the puck’s velocity, as observed by Mario?

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$v_{P W}=5.22 \mathrm{m} \cdot \mathrm{s}^{-1}$$\theta_{1}=52.2^{\circ}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

Simon Fraser University

Hope College

University of Sheffield

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.

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03:34

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01:19

A hockey puck is traveling…

So the question states that Mario is skating directly south at seven meters per second and his teammate hits him the puck, an angle of 22 degrees west of south like this. 22 degrees at a speed of 11 meters per second. And our goal is to find what the magnitude and the direction of the puck is as observed from Mario at this point here. So since we know that the puck is described by this vector and Mario is described by this vector here, we can figure out the magnitude in the direction of the puck as observed from Mario, using this vector here, which describes this relationship. So if we want to find this vector that connects these two end points, we have to subtract the vector that describes the puck and the victor that describes Mario. So let's let's write these two vectors down. So the vector that the that describes Mario Weaken right as zero were saying, The X direction is east to West, um, and East is positive and West is negative, and the vertical direction, uh, is north. The south, where North is positive, sounds negative. So the vector that describes um, Mario is motion is gonna be zero because he has no east west motion negative seven meters per second because he's moving down. And the vector that describes the motion for, uh, the puck we can write down as negative 11 sign of 22 degrees and negative 11 co sign of 22 degrees. And I figure this out because let me draw the victor over here might make some more sense. So we know that the angle here is 22 degrees, and we know that this is 11 meters per second. So if we want to find the horizontal and vertical component of this vector, we know that sign of 22 degrees is equal to opposite over. I pon you. So we're calling this visa vex, and this is a visa. By So opposite is Visa, Becks over 11 meters per second and you can solve for a visa, bex. It's just gonna be 11 signed 22 degrees and the same thing goes for visa. Why accept or using, uh, co sign of 22 degrees, be supply over 11 meters per second. So you see where we get this this relationship here from So if we subtract thes two vectors, we end up getting the vector. So we're subtracting these. We get the victor 11 sign, 22 degrees and then negative seven plus 11 co sign 22 degrees. So now that we have this vector, we confined the magnitude of the, um this vector here, which was called B um, So take the magnitude. We just take the square root of this X component squared. So 11 sign, 22 degrees squared and add it to the y component squared. So negative seven. Call us 11 co sign 22 degrees squared all under the square root. And when we do this, we find out that the velocity of, uh, this vector here is 5.22 meters per second. So this is the magnitude that we were looking for for the philosophy as observed by Mario of the book. So now that we have this, we can try to figure out what the direction is of the book, as seen from due West, as seen from Mario. So I think the best way to probably approach this is to redraw the picture. So let's look here. So this is our velocity vector that is connecting. Mario is velocity here and the, uh, pucks velocity. So we know this velocity vector here is 5.22 meters per second. We just calculated that over here, right? And we're trying to find the angle that's described here, so we'll just call this data. This is in the south south direction. Right? So we're trying to find the the angle that this this 5.22 meters per second vector makes with the south direction So we can do this because we know what the vertical are. The horizontal component is of this 5.22 meters per second. Um, vector, is we calculated here? It's 11. Signed 22 degrees. Right. So this is going to be 11 sign 22 degrees. And now that we know this, we can just figure out what, uh, fate is by taking the sine inverse of up. So it's gonna be opposite overhype on news. Assign numbers of 11 sign 22 degrees over 5.22 meters per second, and that will give us this angle, which is equal to, um, 52 point 11 degrees. And this is our final answer

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