Question

On the first swing, a pendulum swings through an arc of length 65 cm. On the successive swing, the length of the arc is 85% of the length of the previous swing.


Find the length of the arc on the fourth swing. Round your answer to the nearest centimeter.


A.221 cm

B.39.918 cm C.33.93 cm D. 165.75 cm

Answer 1

The Correct Answer Is B

Answer 2

B. 39.918 cm

Explanation:

We know that the length of the first swing, the arc is 65 cm, and the successive swing the arc is 85% of the length of the previous swing.

The problem is asking for the length of the arc on the fourth swing:

We know that the arc of every consecutive swing will be 85% of the swing before, and we know that 85% = 0.85

So the length of the arc of the second swing will be:

85% * length of the arc on the first swing, or

0.85 * 65 cm = 55.25 cm

Now, to know the length of the arc on the third swing we multiply the length of the arc on the second swing times 0.85:

0.85 * 55.25 cm = 46.962 cm

And finally, the length of the arc on the fourth swing will be the length of the arc in the third swing times 0.85:

0.85 * 46.962 cm = 39.918 cm