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Hello,

This is my problem and the solution from the book. I don't understand how they came to the solution. I believe it's wrong and I offer my own solution(but incomplete). I would appreciate if you could explain how they arrived to their solution or if I'm right. Thanks:)

Please see below

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 (-22.5 i + 20.2j) m/s^2. At

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.

http://photos-a.ak.fbcdn.net/hphotos-ak-snc1/hs030.snc1/3190_91017112564_509877564_2512520_5779508_n.jpg [Broken]

First of all, the angle seems to be in a wrong place. A friend suggested that they ran out of space and put it below x-axis instead of under the ).

Second, I don't understand their reason for breaking total acceleration into components and using them in calculation of Ac.

My attempt at solving this was this.

TotalA = A.radial(Ar) + A.tangential (At) Because all 3 are vectors, then either the i or j is Ac. I believe this is uniform circular motion where v stays the same all the time, so At = 0. then Ac = totalA ?

However, the book gives a different answer, and I cannot imagine how they came up with this odd relationship between 2 vectors.

Please help me with this one.

P.S. this is not my home work (it's just a problem I found in my book while preparing for a final exam.), but I'm worried something like that will be on my final.

Thank you in advance.

R.M.

This is my problem and the solution from the book. I don't understand how they came to the solution. I believe it's wrong and I offer my own solution(but incomplete). I would appreciate if you could explain how they arrived to their solution or if I'm right. Thanks:)

Please see below

## 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 (-22.5 i + 20.2j) m/s^2. At

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.

**2. Solution from the book**http://photos-a.ak.fbcdn.net/hphotos-ak-snc1/hs030.snc1/3190_91017112564_509877564_2512520_5779508_n.jpg [Broken]

**3. My Confusion :-)**First of all, the angle seems to be in a wrong place. A friend suggested that they ran out of space and put it below x-axis instead of under the ).

Second, I don't understand their reason for breaking total acceleration into components and using them in calculation of Ac.

## The Attempt at a Solution

My attempt at solving this was this.

TotalA = A.radial(Ar) + A.tangential (At) Because all 3 are vectors, then either the i or j is Ac. I believe this is uniform circular motion where v stays the same all the time, so At = 0. then Ac = totalA ?

However, the book gives a different answer, and I cannot imagine how they came up with this odd relationship between 2 vectors.

Please help me with this one.

P.S. this is not my home work (it's just a problem I found in my book while preparing for a final exam.), but I'm worried something like that will be on my final.

Thank you in advance.

R.M.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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