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Parametric Equations HW: 11.1; 3,22 Why do we need parametric equations? • Consider the flight of a golf ball…the motion consists of two independent parts (Galileo’s “big” insight): • Falling motion or Galileo’s Law of falling bodies in the vertical (y) direction • Uniform translational motion in the horizontal (x) direction “In Math”… • Vertical motion: • Horizontal motion: 1 2 y(t ) vy t gt 2 “t” is the parameter x(t ) vx t What path does a golf ball follow? 140 120 x(m),y(m) 100 80 60 40 y(t) = -4.905t2 + 20t 20 0 0.0 1.0 2.0 3.0 4.0 5.0 t(s) But how are x and y related to each other? A famous historical example … the Cycloid • What path does a point on the rim of a circle trace as the circle rolls at a constant rate without slipping? So, why do we need parametric equations? • By finding the suitable parameterization you can sometimes express relationships between variables that would otherwise be very difficult to do. Next lecture… • Applying ideas of calculus to parametric equations • Read 11.2 • HW: 3, 15