lecture_5_302k - linear combination of these two unit...

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PHY 302K Rob Clark Lecture #5 Outline September 3, 2010 1. Homework quiz; web homework was due at noon today. Homework #2 is out today and due next Friday at noon. 2. Motion in two dimensions In the demo, we notice that the projectile changes velocity, meaning it has experienced an acceleration. However, its velocity in the x direction is such that it meets the cart on the other side. The only acceleration is along the y direction. This means we need a way to mathematically treat the two directions independently. 3. Vectors are such a mathematical tool. A vector is a quantity that has both magnitude (length) and direction. In one dimension, the absolute value of a quantity is its magnitude and its sign is the direction. In two or more dimensions, a vector quantity can be written in terms of unit vectors . These have magnitude of 1. Normally, we choose to use unit vectors that point along the cartesian axes. The book has these as i-hat and j-hat; I prefer to use x-hat and y-hat. Any vector in 2-D can be written as a
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Unformatted text preview: linear combination of these two unit vectors. A vector can also be expressed as a magnitude and direction. For doing algebra with vectors, the component form is much better. For thinking about vectors geometrically, you may prefer to use magnitude and direction. Please read Sec. 3.1 and 3.2 for information on switching between component and magnitude/ direction representations of a vector. 4. Motion in 2-D We find that, at least for the case of projectile motion, the x and y coordinates of a particle obey the equations for motion under constant acceleration separately. We use this in class to figure out at what angle to fire a projectile to obtain a maximum distance along the horizontal. We also go monkey hunting. You will want to ask about this if you missed class. Please read the rest of Chapter 3; it will be indispensable for the homework....
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