Answer:
25.13 inches per second
Step-by-step explanation:
The formula for linear velocity is:
[tex]v=\frac{2\pi r}{T}[/tex]
Where [tex]r[/tex] is the radius, and [tex]T[/tex] is the period of oscilation.
The radius is:
[tex]r=40feet[/tex] but because we need the answer in inches per second we need to convert this to inches (1 feet = 12 inches):
[tex]r=40*12in\\r=480in[/tex]
and the Period is the time it takes to complete a revolucion:
[tex]T=\frac{12minutes}{6revolutions}\\ T=2minutes/revolution[/tex]
it takes 2 minutes to complete 1 revolution. Again, since we need the result in inches per second we need to convert the Period to seconds (1 minute = 60 seconds)
[tex]T=2*60seconds/revolution\\T=120seconds/revolution[/tex]
substituting our values for the linear velocity:
[tex]v=\frac{2\pi r}{T}[/tex]
[tex]v=\frac{2\pi (480inches)}{120seconds} \\v=25.13inches/second[/tex]
the linear velocity is 25.13 inches per second
