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28 A physical quantity is a physical property of a phenomenon body or subs by measurement 34 The magnitude of the components of a vector are to be considered dimensionally distinct For example rather than an undifferentiated length unit L we may represent length in the x direction as L and so forth This requirement stems ultimately from the requirement that each component of a physically meaningful equation scalar or vector must be dimensionally consistent As an example suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V and of width D and he is swimming in direction perpendicular to the river flow with velocity V relative to river L T assuming no use of directed lengths the quantities of interest are then V V both dimensioned as S the drift and D width of river both having dimension L With these four quantities we may conclude that the equation for the drift S may be written So VaVbDc y Or dimensionally L x L from which may deduce that a b c 1 and a b 0 which leaves one of these exponents undetermined If however we use directed length dimensions then V will be dimensioned as Ly V as S as L and D as L The dimensional equation T T becomes L a b and we L and we may solve completely as a 1 b 1 and c 1 The increase in deductive power gained by the use of directed length dimensions is apparent Which of the following is not a physical quantity A Height of a boy C Fever of a boy A R 29 From the concept of directed dimension what is the formula for a range R of a cannon ball when it is fired with vertical velocity component V and a horizontal velocity component V assuming it is fired on a flat surface Range also depends upon acceleration due to gravity g and k is numerical constant k V V g B R B Weight of a boy D Speed of a running boy k V g R C R k V Vyg D R k V V g

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