Question

A child is given an initial push on a rope swing. On the first? swing, the rope swings through an arc of

6

feet. On each successive? swing, the length of the arc is

90?%

of the previous length. After

15

?swings, what total length will the rope have? swung? When the child stops? swinging, what total length will the rope have? swung?

Answer 1

Given, on the first swing, the rope swings through an arc of 6 feet and on each successive swing, the length of the arc is 90% of the previous length.

Then, after 15 swings, the total length the rope will have swung is = [6+6*(0.9)+6*(0.9)²+....+6*(0.9)¹⁴] feet

= [6*(1-0.9¹⁵)/(1-0.9)] feet

47.65 feet

Now, after n swings, the total length the rope will have swung is = [6*(1-0.9ⁿ)/(1-0.9)] feet

= [60*(1-0.9ⁿ)] feet

when n , then 60*(1-0.9ⁿ) 60

Therefore, when the child stop swinging, then the total length the rope will have swung is 60 feet.