Answer
The radius of the rear sprocket is 2.99 cm.
Work Step by Step
We can find the angular speed of the rear sprocket. Let $v_r$ be the tangential speed of the rear wheel.
$\omega = \frac{v_r}{r} = \frac{5.00~m/s}{0.330~m}$
$\omega = 15.15~rad/s$
We can find the tangential speed of the rear sprocket. Let $\omega_f$ be the angular speed of the front sprocket.
$v = \omega_f ~r$
$v = (0.600~rev/s)(2\pi~rad/rev)(0.120~m)$
$v = 0.4524~m/s$
We can find the radius of the rear sprocket.
$r = \frac{v}{\omega} - \frac{0.4524~m/s}{15.15~rad/s}$
$r = 0.0299~m = 2.99~cm$
The radius of the rear sprocket is 2.99 cm.
