2-D vector analysis help

1. The problem statement, all variables and given/known data

http://ift.tt/1jlF3so

2. Relevant equations

I have the solutions and how they did it. THey took the deriv for the velocity vector, and then using t=0 and t=14, they found e=3.5 and f=-0.125

3. The attempt at a solution

I understand the math, but I don’t understand why this is correct
1) why did they take the velocity vector?
2) if I plug e and f back into the position vector, and using t=14 i should get θ=0, ie, j-component is 0. But I don’t. So what am I doing wrong?

http://ift.tt/1jlF5jS

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