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Essential University Physics: Volume 1 (Ch3,4,&5)

Essential University Physics: Volume 1 (Ch3,4,&5) -...

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Unformatted text preview: Motion in TWO _Jml Tl At what angle should this penguin leave the terto maximize the range of its jump? hat's the speed of an orbiting satellite? How should I leap to win the long—jump competi— tion? How do | engineer a curve in the road for safe driving? These and many other ques- tions involve motion in more than one dimension. in this chapter we extend the ideas of one-dimensional motion to these more complexkand more interesting—situations. 3.1 Vectors We’ve seen that quantities describing motion have direction as well as magnitude. In Chapter 2, a simple plus or minus sign took care of direction. But now, in two or three di— mensions, we need a way to account for all possible directions. We do this with mathemat- ical quantities called vectors, which express both magnitude and direction. Vectors stand in contrast to scalars, which are quantities that have no direction. Position and Displacement The simplest vector quantity is position. Given an origin, we can characterize any position in space by drawing an arrow from the origin to that position. That arrow is a pictorial rep— resentation of a position vector, which we call F. The arrow over the r indicates that this ...
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