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Two friends, Barbara and Neil, are out rollerblading. With respect to the ground, Barbara is skating due south at a speed of 4.0 m/s. Neil is in front of her. With respect to the ground, Neil is skating due westat a speed of 3.2 m/s. Find Neil’s velocity (magnitude and direction rel- ative to due west), as seen by Barbara.

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(a) $v_{N B}=5.12 \mathrm{m} \cdot \mathrm{s}^{-1}$(b) $\theta=51.34^{\circ}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Washington

Simon Fraser University

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.

04:35

Two friends, Barbara and N…

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So the question states that Neil is moving at 3.2 meters per second due west, while Barbara is moving at four meters per second due south. And we're trying to find the magnitude and direction of the velocity of Neil, as seen from Barbara Barbara relative to Due West. So we can see in this diagram. Deal is moving west and Barbara is moving self. And there's this vector here. We'll call it V that connects the two and this condition scribe the velocity of Neil, as seen from Barbara So defined this vector v here. We just have to add the two victors, um, of Barbara and Neil. And to do this, we can take the square root of four squared plus 3.2 squared, and this will give us V wish will be equal to 5.12 meters per second. And then to find what this angle fatal here is, which is the angle of the vector relative to due West. We first confined what this angle is here by taking the tan in verse of 3.2 over four. And once we do this, we find that we get 38 point 66 degrees as this angle here and then we consider weaken. Take 90 degrees and subtract this angle, and that will give us the angle relative to due West from due West. So 90 minus 38 0.66 will give us 51.34 degrees, and that's the answer.

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