Acceleration and cylindrical coordinates

[abdo799]

Homework Statement

The question and my attempt are attached as pics

Homework Equations

The Attempt at a Solution

I can't seem to find r¨ and θ¨. Assuming I already got r˙ and θ˙ (the answers are written after the question). The idea I tried was to get the acceleration equation in cylindrical coordinates,
a=(r¨−rθ˙2)r^+(rθ¨+2θ˙r˙)θ^
and the a in intrinsic coordinates (v˙t^+v2/ρn^) in our case I assumed that t^=i and n^=j and that assumption is correct because it got the r˙ right, then I got r^ and θ^ in terms of i and j and now we have 2 equations with 2 unknown. The problem is that it gets the answer wrong, I checked my numbers a trillion time, still can't get the answer, anyone have any idea what is wrong?

 

[haruspex]

I see nothing wrong with your method or working. Did you find $\dot r$ and $\dot \theta$ independently, or are you just using the numbers given? What numbers do you get for the second derivatives?

 

[abdo799]

I see nothing wrong with your method or working. Did you find $\dot r$ and $\dot \theta$ independently, or are you just using the numbers given? What numbers do you get for the second derivatives?

i managed to get $\dot r$ and $\dot \theta$ but i didnt include it here, i am going to use the given numbers for now, the question asks for second derivatives he gave me the answers but they don't match mine