Question

If you are riding on a Ferris wheel that is 60 feet tall and it takes you 5 minutes to make one revolution, what is your linear velocity?
a. 0.62 feet per second
b. 0.31 feet per second
c. 37.68 feet per second
d. 3.14 feet per second
e. 9.42 feet per second

Answer 1

By definition, the linear velocity is given by:
 $v = w*r$
 Where,
 w: angular speed
 r: radius
 We have that the radius of the wheel is
 $r = d / 2$
 Where,
 d: diameter of the wheel
 substituting values:
 $r = 60/2 r = 30 feet$
 Then, we have the following conversions:
 1 revolution = 2π radians
 1 minute = 60 seconds
 Therefore, the angular velocity in radians per second is:
 $w = \frac{1}{5} \frac{2 \pi }{60}$
 $w = 0.0209 \frac{rad}{s}$
 Substituting values we have:
 $v = (0.0209)(30) v= 0.62$
 Answer:
 your linear velocity is:
 a. 0.62 feet per second