Follow that dot

Calculus Level 3

The coordinates of a dot \(P\) moving in the \(xy\) plane at time \(t\) are given by: \(x = 5e^{-t}\cos t\) and \(y = 5e^{-t} \sin t\). Let \(L_a\) be the distance traveled by \(P\) in the interval \(0 \leq t \leq a\). If \(\displaystyle \lim_{a \to \infty} L_a = z\), what is the value of \(z^2\)?

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