By J. S. Marshall, E. R. Pounder, R. W. Stewart (auth.)
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6 miles up ADDITION OF VECTORS 29 Note two things: (1) Three numbers are needed. (2) At least one of these numbers must have dimensions of length. Displacement is the first of many quantities we shall encounter which require at least two numbers to specify them: one number to measure size and one to give direction. They are referred to as vector quantities and are to be contrasted with most of the familiar quantities in everyday life which have size or magnitude only. Such things as the mass of a bag of sugar, the volume of a room, the number of students in a class, the amount of money in your pocket, are completely described by a number together with the unit in which the number is measured.
There would be no tendency for the errors to cancel each other. Such an error is called a systematic error, or bias. With a systematic error the most probable over-all error is no longer zero. A different illustration is instructive here: Suppose three men, using different rifles, are firing at targets. Suppose also that they have no way of knowing where their shots are hitting. One man is a good shot, and his rifle sights are well aligned. 05(a). A second man also has well-aligned sights, but is not such a good shot.
Join KINEMATICS 48 OL, OM, ON, OP, etc. ; for example, for v = ON v = ON = OC + CN = 3a + OK = 3a + = u + 3a u A similar process can be used to solve the equation d = ut + iat2 , only in this case it is a displacement diagram that is being drawn rather than a velocity diagram. Choose scale as (say) 1 cm = 2 m. Draw O'X' in direction of acceleration and O'K' in direction of u. Calculate magnitudes of ut and tat 2 for various values of t and plot these values to scale along O'X' and O'K'. 13. 00 To find the displacement at any of these times, we add the two components by the parallelogram law as indicated by the dotted lines.