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Find min. speed and direction of velocity, given parametric eqns

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A hockey puck of radius 1 slides along the ice at a speed 10 in the direction of the vector (1,1). As it slides, it spins in a counterclockwise direction at 2 revolutions per unit time. At time t = 0, the puck’s center is at the origin (0,0).

    Find the parametric equations for the trajectory of the point P on the edge of the puck initially at (1,0).

    radius = R = 1
    frequency = f = 2
    angular frequency = w = 2πf = 4π
    θ = wt

    Thus, I found r(t) = (cos4πt + 5sqrt2t, sin4πt + 5sqrt2t)

    Now that I have the equation of the trajectory, how do I find the minimum speed of the point P, and the direction of the velocity at the corresponding time?

    2. Relevant equations

    3. The attempt at a solution
    Velocity: v(t) = (-4πsin4πt + 5sqrt2, 4πcos4πt + 5sqrt2)
    v’(t) = (-16π2cos4πt, -16π2sin4πt) = 0
     
  2. jcsd
  3. Nov 17, 2009 #2
    The puck is rotating so its acceleration is never zero; however it is easy to guess that the speed of P is extremized when the speed due to rotation is to the same direction as the linear movement.
     
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