Question

problem 4: a carousel at the theme park goes around once every 55 seconds. given that the radius of the carousel is 6.2 meters, how much distance has a horse on the edge traveled after 30 seconds?

Explanation:

Step1: Calculate the circumference of the carousel

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 6.2\) meters, we have \(C=2\pi\times6.2= 12.4\pi\) meters.

Step2: Find the fraction of the full - rotation in 30 seconds

The carousel makes one full rotation in 55 seconds. The fraction of the rotation in 30 seconds is \(\frac{30}{55}=\frac{6}{11}\).

Step3: Calculate the distance traveled

The distance \(d\) traveled is the fraction of the rotation times the circumference. So \(d=\frac{6}{11}\times12.4\pi\).

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Answer:

The horse on the edge has traveled approximately \(21.24\) meters.