Formula for the circumference of a circle:
C = 2πr (C = circumference π(pi) = 3.14..... r = radius)
You know:
r = 9 cm
π = 3.14 So substitute/plug it into the equation
C = 2πr
C = 2(3.14)(9)
C = 56.52 cm
One revolution is completed when a fixed point on the wheel travels a distance equal to the circumference of the wheel, which is 2π (13 cm) = 26π cm.
So we have
1 rev = 26π cm
1 rev = 2π rad
1 min = 60 s
(a) The angular velocity of the wheel is
(35 rev/min) * (2π rad/rev) * (1/60 min/s) = 7π/6 rad/s
or approximately 3.665 rad/s.
(b) The linear velocity is
(35 rev/min) * (26π cm/rev) * (1/60 min/s) = 91π/6 cm/s
or roughly 47.648 cm/s.
Overall, they spent 3 3/4 hours fishing and swimming.
