Problem 1: Consider a particle whose motion is described with the position vector: r (t) = ˆi2c cos𝞈t + ˆjc sin𝞈t, Where c and 𝞈 are constants. (a) Show that the path of the particle is an ellipse satisfying. x2/a2 +y2/b2 = 1, Where x and y are the cartesian coordinates of the particle. State the values of a and b in terms of c. (b) Find the velocity of the particle. What is the rotation direction, clockwise or counter-clockwise? (c) At tmin and tmax, the distance of the particle from the origin is minimum and maximum, respectively. Find tmin and tmax. Note: (that since the motion is periodic, there are infinitely many tmin and tmax values). State the ones in the interval t ∊ [0,Π/𝞈] Calculate the velocities corresponding to tmin and tmax. (d) Show that a = - 𝞈 2 r, (e) Show that h = r x v, is constant by directly calculating it. Notice that the

Question

Problem 1: Consider a particle whose motion is described with the position vector:                                                   r (t) = ˆi2c cos𝞈t + ˆjc sin𝞈t, Where c and 𝞈 are constants.  (a)	Show that the path of the particle is an ellipse satisfying.                                                  x2/a2 +y2/b2 = 1, Where x and y are the cartesian coordinates of the particle. State the values of a and b in terms of c.       (b) Find the velocity of the particle. What is the rotation direction, clockwise or counter-clockwise?        (c) At tmin and tmax, the distance of the particle from the origin is minimum and maximum, respectively. Find  tmin and tmax.   Note: (that since the motion is periodic, there are infinitely many tmin and tmax values). State the ones in the interval        t ∊ [0,Π/𝞈]  Calculate the velocities corresponding to tmin and tmax.       (d) Show that             a = - 𝞈 2 r,        (e) Show that             h = r x v,  is constant by directly calculating it. Notice that the