Question

Oscillation 1 2 3
Distance 8 6 ?
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?
(1 point)
3 feet
4 feet
5 feet
4.5 feet

Answer 1

To determine the distance the swing will travel in the third oscillation, we can follow the pattern described.

1. The first oscillation travels a distance of 8 feet.
2. The second oscillation travels \(\frac{3}{4}\) of the distance of the first oscillation:
\[
\text{Distance of 2nd oscillation} = 8 \times \frac{3}{4} = 6 \text{ feet}
\]
3. The third oscillation will travel \(\frac{3}{4}\) of the distance of the second oscillation:
\[
\text{Distance of 3rd oscillation} = 6 \times \frac{3}{4} = 4.5 \text{ feet}
\]

Now we can round \(4.5\) feet to the nearest whole number, which is **5 feet**.

Thus, the answer is:
**5 feet**.