A rock tied to a rope moves in the xy-plane. Its coordinates are given as functions of time by s(t) = R cos wt y(t) = R sin wt where R and", are constants.
(a) Show that the rock's distance from the origin is constant and eqna1 to R-that is, that its path is a circle of radius R.
(b) Show that at every point the rock's velocity is perpendicular to its position vector.
(c) Show that the rock's acceleration is always opposite in direction to its position vector and has magnitude w2R.
(d) Show that the magnitude of the rock's velocity is constant and equal to wR.
(e) Combine the results of parts (c) and (d) to show that the rock's acceleration has constant magnitude v2/R