Question

# A child is given an initial push on a rope swing. On the first? swing, the...

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?

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.

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