Problema Solution
Assume that a very long rope supported by poles that are 2 feet
tall is stretched around the moon. (Neglect gravitational pull and
assume that the rope takes the shape of a large circle.) The radius
of the moon is approximately 1080 miles. How much longer would
you need to make the rope if you wanted the rope to be supported
by poles that are 6 feet tall? (Use 3.14 to approximate pie.).
Answer provided by our tutors
let
r = 1080 miles = 1080*5280 ft the radius of the moon (since 1 mile = 5280 ft)
pi = 3.14
the length of the rope with 2 ft poles is
P1 = 2(r+2)pi
the length of the rope with 6 ft poles is
P2 = 2(r+6)pi
the difference in lengths is P2 - P1 = 2(r+6)pi - 2(r+2)pi = 2pi(r + 6 - r - 2) = 2pi*4 = 8*pi = 8*3.14 = 25.12 ft
the rope needs to be longer by 25.12 ft.