Question

A student walks forward a distance represented by the displacement vector A of magnitude 5.3 m, and then walks to obtain an additional displacement B of length 4.1 perpendicular to A. (a) What is the magnitude of the resulting displacement from the origin? (b) What magnitude of total displacement would result if the second displacement were -B instead of B? Conceptualize The length of the arrow representing displacement vector A is proportional to the distance of 5.3 m that A represents, and there is a second displacement EB that is perpendicular to A reverse of length 4.1 m. Display in a New Window
(A) The magnitude of the displacement from the origin Analyze If we sketch a diagram showing the vector addition, with the tail of B appended to the arrowhead representing A, then it becomes clear that the Pythagorean theorem must be used to find the length of R which is then the resulting magnitude of the displacement. It is equal to (B) The magnitude when B is changed to B. Analyze In this case, we can add -B to A, instead of adding B to A. This then becomes Finalize The greatest magnitude for A + B results when the two directions are (the same/opposite/perpendicular) the same? The smallest magnitude for A + B results when the two directions are (the same/opposite/perpendicular) opposite
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