Serway & Jewett — Motion in Two Dimensions: Problem 24

A ball swings counterclockwise in a vertical circle at the end of a rope $1.50\text{ m}$ long. When the ball is $36.9^\circ$ past the lowest point on its way up, its total acceleration is $(-22.5 \hat{i} + 20.2 \hat{j})\text{ m/s}^2$. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.