Answer
25.316
Work Step by Step
Since speed is given by
\begin{align*}
\frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\
&=\sqrt{(15)^2 \cos 5t+( 40)^2 \sin^2 5t }
\end{align*}
Then
\begin{align*}
\frac{d s}{d t}\bigg|_{t= 2} &=\sqrt{(15)^2 \cos 5\pi/4+( 40)^2 \sin^2 5\pi/4 } \\
&=\sqrt{-\frac{225\sqrt{2}}{2}+800}\approx 25.316
\end{align*}
