Question

1. when you are out fishing, you notice that every time you throw your line in, a circular ripple is produced. what is the spread of the circular ripple after 30 seconds? if the ripple travels outward at a speed of 60 cm/s?

the spread of the circular ripple after 30 seconds is 1,317,032.9 cm²?
the spread of the circular ripple after 30 seconds is 3,600,007.5 cm²?
the spread of the circular ripple after 30 seconds is 900.87 cm²?
the spread of the circular ripple after 30 seconds is 10,170,751.6 cm²?

Explanation:

Step1: Find the radius after 30 seconds

The speed of the ripple is \(v = 60\) cm/s. Using the formula \(r=v\times t\) (where \(t = 30\) s), we get \(r=60\times30 = 1800\) cm.

Step2: Calculate the area of the circular ripple

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 1800\) cm and taking \(\pi\approx3.14159\), we have \(A = 3.14159\times(1800)^{2}\).

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Answer:

The spread of the circular ripple after 30 seconds is \(10,178,751.6\space cm^{2}\) (the first option).