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

1. Nov 17, 2009

### plexus0208

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).

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. Nov 17, 2009

### clamtrox

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.