Question

A stone is tossed into a pond, creating a circular ripple. The radius of the rippleincreases by 12cm/s.a) Write an equation that describes the ripple exactly 3 s after the stone lands in thewater. Use the origin as the point where the stone lands in the water.b) A canoe is located at point (-36, 48). When will the ripple reach the canoe?

Answer 1

SOLUTION

The given increase in radius is 12cm/s

The after 3 secods the radius of the ripple will be

$\begin{gathered} R=r\times t \\ R=\frac{12cm}{s}\times3s \\ R=36cm \end{gathered}$

b. A canoe is located at (-36,48)

Consider the image shown below

By using the Pythagorean theorem it follows

$\begin{gathered} R^{}=\sqrt[]{48^2+36^2} \\ R=\sqrt[]{2304+1296} \\ R=\sqrt[]{3600} \\ R=60 \end{gathered}$

To get how long it will take the ripple to reach the cone, divide R by 12

This gives

$\frac{60}{12}=5$

Therefore, it will take the ripple 5 seconds to get to the canoe