Exercise 1.3.59

Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 $\mathrm{cm} / \mathrm{s}$.
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(a) Express the radius $r$ of this circle as a function of the time $t$ (in seconds).
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(b) If $A$ is the area of this circle as a function of the radius, find $H\circ r$ and interpret it.

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]

\item $$\forall t \in[0,+\infty): r(t)=60 t.$$

\item $$\forall r \in[0,+\infty): A(	au)=\pi r^{2}$$
$$\forall t \in[0,+\infty): A \circ r(t)=3600 \pi t^{2}$$

The function $A \circ r$ of the time $t$ represents the circular ripple area at the particular time $t$.
\end{enumerate}

Exercise 1.3.59

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Exercise 1.3.59

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