mat-sln-asn-hwk18-spr02 - vector into components parallel...

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Solution for Homework 18 Motion in a Plane II Solution to Homework Problem 18.1() Problem: What is the efect oF adding multiple vectors (in two dimensions) in diferent orders? (Will the end result oF each combination be the same or diferent?) Is the same true For subtraction? Solution Vector addition is commutative, which means that For any two vectors va and v b , va + v b = v b + va So you can add vectors in any order you want, and you will get the same answer. Vector subtraction, in general, is not commutative. In other words, va v b n = v b va So iF you switch the order oF subtraction, you will not get the same answer (except in special cases, oF course, like when va = v b ). Total Points for Problem: 2 Points Solution to Homework Problem 18.2() Problem: Why do we restrict our study oF acceleration’s efects upon velocity in two dimensions to a short time Frame? Solution In two dimensional motion, we can analyze the change in velocity due to an acceleration by decomposing the acceleration
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Unformatted text preview: vector into components parallel and perpendicular to the velocity vector. Instantaneously, the parallel component oF acceleration afects only speed (increasing speed iF parallel to velocity, decreasing speed iF antiparallel), and the perpendicular component afects only the direction oF the velocity vector. In general, however, these quantities change with time, so this analysis only makes sense iF considered over a very short time interval. ±or example, iF the acceleration vector is constant in time but not parallel to the velocity vector, then the direction and magnitude oF the velocity vector change with time, and so the components oF acceleration (with respect to the velocity vector) change with time as well (even though their vector sum stays the same). Total Points for Problem: 2 Points...
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This note was uploaded on 05/04/2008 for the course PHYS 2054 taught by Professor Stewart during the Spring '08 term at Arkansas.

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