How Do You Calculate Radial Acceleration and Velocity in Circular Motion?

[yitriana]

Homework Statement

A ball swings in a vertical circle at the end of a rope 1.50 m
long. When the ball is 36.9° past the lowest point on its
way up, its total acceleration is (-22.5i, 20.2j) m/s2. At
that instant, (a) determine the magnitude
of its radial acceleration, and (b) determine the speed and
velocity of the ball.

Homework Equations

a = v²/r

The Attempt at a Solution

Centripetal acceleration resolved into two components, in x direction, -22.5 and y direction, 20.2. I would think that in order to get the net acceleration, just (22.5^2 + 20.2^2)^0.5. However, this yielded an incorrect solution. Why doesn't this work and what is the correct approach?

 

[LowlyPion]

I think they give you the acceleration vector in x,y, but you also have a component from gravity in the vertical direction to take into account, don't you?

So you have 2 ways to figure it.

1) observe that tanθ = i/j and use the i component to resolve the unknown j or
2) add 9.8 to the j