![]() Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the From the geometry in Figure 4.29, we can solve easily for the magnitude of the velocity of the plane with respect to the ground and the angle of the plane’s heading, θ. The vector equation is v → PG = v → PA + v → AG, v → PG = v → PA + v → AG, where P = plane, A = air, and G = ground. The diagram will also tell us the angle the plane’s velocity makes with north with respect to the air, which is the direction the pilot must head the plane. We can graph the vectors and use this diagram to evaluate the magnitude of the plane’s velocity with respect to the ground. Since these last two quantities are known, we can solve for the velocity of the plane with respect to the ground. ![]() We need to construct a vector equation that contains the velocity of the plane with respect to the ground, the velocity of the plane with respect to the air, and the velocity of the air with respect to the ground. The pilot must point the plane somewhat east of north to compensate for the wind velocity. (a) In what direction must the pilot head the plane to fly due north? (b) What is the speed of the plane relative to the ground? A wind is blowing out of the northeast at 90 km/h. The plane can fly at 300 km/h in still air. This relative velocity is written asĪ pilot must fly a plane due north to reach their destination. We can add the two velocity vectors to find the velocity of the person with respect to Earth. Since the person is walking west, in the negative direction, we write her velocity with respect to the train as v → PT = −2 m / s i ^. This tells us she has a velocity relative to the reference frame of the train. Let’s now say the person gets up out of her seat and walks toward the back of the train at 2 m/s. If we choose east as the positive direction and Earth as the reference frame, then we can write the velocity of the train with respect to the Earth as v → TE = 10 m / s i ^ v → TE = 10 m / s i ^ east, where the subscripts TE refer to train and Earth. Take the example of the person sitting in a train moving east. We introduce relative motion in one dimension first, because the velocity vectors simplify to having only two possible directions. This method makes an approximation that breaks down near the speed of light, where the more accurate methods or special relativity are needed, but is extremely accurate for everyday speeds ( Relativity). We now develop a method to refer to reference frames in relative motion. In summary, all discussion of relative motion must define the reference frames involved. In this case, the solar system is the reference frame. We can expand our view of the motion of the person on the train and say Earth is spinning in its orbit around the Sun, in which case the motion becomes more complicated. ![]() If you say a person is sitting in a train moving at 10 m/s east, then you imply the person on the train is moving relative to the surface of Earth at this velocity, and Earth is the reference frame. ![]() In most examples we have examined so far, this reference frame has been Earth. When we say an object has a certain velocity, we must state it has a velocity with respect to a given reference frame. To discuss relative motion in one or more dimensions, we first introduce the concept of reference frame s. To explore this idea further, we first need to establish some terminology. Your velocity relative to the other train is 5 m/s west. However, if another train passes you at 15 m/s east, your velocity relative to this other train is different from your velocity relative to the ground. If you’re riding in a train moving at 10 m/s east, this velocity is measured relative to the ground on which you’re traveling.
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