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SSM Two passenger trains are passing each other on adjacent tracks. Train A is moving east with a speed of 13 m/s, and train B is traveling west with a speed of 28 m/s. (a) What is the velocity (magnitude and direction) of train A as seen by the passengers in train B? (b) What is the velocity (magnitude and direction) of train B as seen by the passengers in train A?

(a) $\vec{v}_{A B}=+41 \mathrm{m} \cdot \mathrm{s}^{-1},$ east.(b) $\vec{v}_{B A}=-41 \mathrm{m} \cdot \mathrm{s}^{-1},$ west.

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

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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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SSM Two passenger trains a…

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So the question states that two trains are moving in opposite directions. Train A is moving east at a speed of 13 meters per second and a and we're saying the origin here is the ground Well trained, um, B is moving at 28 meters per second west and our goal is to find, um first off what? The speed of train A is relative to train and be so if we take our point starting here at train be this is the point, that is ah, relative to trend be and we connect it to the victor on train A We see that the ah speed that train a is moving relative to train be It's just the vector of 28 meters per second plus the vector of 13 meters per second. Now, of course, uh, this vector here would be superimposed on the x axis, but I just threw it often decide to make it a little bit more clear. So this vector is 28 plus 12 which is equal to 41 meters per second in the positive direction. So that is the speed that training is moving relative to a person standing on train be so now. So you were standing on train? A. So you're standing here and you were observing trained be defector that connects all the way over to train be is once again 48 or 41 meters per second, but it's in the negative direction, so in the westerly direction, and that's the final answer.

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