Question 768502
THe circumference of a circle with radius {{{r}}} can be calculated as {{{2pi*r}}}.
The inner circular path has a length (circumference) of
{{{2pi(32feet)}}}= approx. {{{201.0619feet}}}.
The outer circular path has a length (circumference) of
{{{2pi(38feet)}}}= approx. {{{238.7610feet}}}
The difference in length is {{{238.7610feet-201.0619feet=37.6991feet}}}.
Converting into miles:
{{{37.6991feet(1mile/5280feet)=37.6991/5280}}}{{{miles}}}
That is the difference in distance traveled by the outer ring of seats over the inner ring of seats as the rides goes through one turn in 3.25 seconds.
Converting into hours:
{{{3.25seconds(1hour/60minutes)(1 minute/60seconds)=3.25/3660}}}{{{hours}}}
The difference in linear velocities is
{{{(37.6991/5280)miles}}} divided by {{{(3.25/3660)hours}}}
{{{(37.6991/5280)miles/((3.25/3660)hours)=(37.6991/5280)(3660/3.25)}}}{{{miles/hour=8.04)}}} miles per hour
miles per hour (rounded to the nearest tenth).
Rounded to the nearest tenth, the linear speed of the swings in the outer ring is {{{highlight("8.0")}}} miles per hour greater than the linear speed of the swings in the inner ring.