Cassandra attempts to do the yo-yo trick 'Around the World

Question

She throws the yo-yo so that it sweeps out a vertical circle whose radius is the length of the yo-yo string. If the yo-yo string is 27 inches long and the distance the yo-yo travels in an arc is 60.29 inches, answer the following questions below. Assume that the yo-yo travels in a perfect circle a. Find the central angle associated with this ard. b. If the yo-yo traveled in one full circle, what is the distance that the yo-yo travels?

Answer 1

27A = 62.9 where A is the angle in radians

A = 62.9/27 = 2.33 radians

180/pi = A/2.33 with A measured in degrees

A=2.33(180)/pi = 133.5 degrees

circumference of a circle = 2pi(r) = 2(3.14159)27 = 54pi = 169.4 inches = the distance the yo yo traveled in one full circle.