Questions: A playground swing sways back and forth and loses momentum and distance with each oscillation. If the swing travels a total distance of 8 feet on the first iteration and the distance of each consecutive oscillation is 3/4 of the previous distance, what distance will the swing travel in the third oscillation, measured to the nearest whole foot? 4 feet 3 feet 5 feet 4.5 feet

A playground swing sways back and forth and loses momentum and distance with each oscillation. If the swing travels a total distance of 8 feet on the first iteration and the distance of each consecutive oscillation is 3/4 of the previous distance, what distance will the swing travel in the third oscillation, measured to the nearest whole foot? 4 feet 3 feet 5 feet 4.5 feet
Transcript text: A playground swing sways back and forth and loses momentum and distance with each oscillation. If the swing travels a total distance of 8 feet on the first iteration and the distance of each consecutive oscillation is $\frac{3}{4}$ of the previous distance, what distance will the swing travel in the third oscillation, measured to the nearest whole foot? 4 feet 3 feet 5 feet 4.5 feet
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given the distances traveled by a swing in the first and second oscillations, and we need to find the distance traveled in the third oscillation. The distance of each consecutive oscillation is \(\frac{3}{4}\) of the previous distance.

Step 2: Calculate the Distance for the Second Oscillation

The distance for the second oscillation is given as 6 feet. We can verify this by calculating: \[ \text{Distance for the second oscillation} = 8 \times \frac{3}{4} = 6 \text{ feet} \]

Step 3: Calculate the Distance for the Third Oscillation

To find the distance for the third oscillation, we use the distance of the second oscillation and multiply it by \(\frac{3}{4}\): \[ \text{Distance for the third oscillation} = 6 \times \frac{3}{4} = 4.5 \text{ feet} \]

Final Answer

The distance the swing will travel in the third oscillation, measured to the nearest whole foot, is: \[ \boxed{5 \text{ feet}} \]

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