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11-68.

SOMETHING'S FISHY
An object moves in the $xy$-plane so that its position at any time $t$, $0 ≤ t ≤ π$, is given by $x(t) = 3\operatorname{cos} 2t$ and $y(t) =\operatorname{ \ln}(1 + t) +\operatorname{ sin} 2t$. Use your graphing calculator to answer the questions below.

1. Sketch the path on graph paper. Indicate the direction of motion along the path.

What does the graph look like?

2. At what $t$ in the given domain does $y$ attain its maximum value?

3. What is the position $(x(t)$, $y(t))$ of the object when y attains its maximum value?

4. Find the acceleration vector.