A small stone with mass m gets stuck in the tread of a rolling tire whose radius is r. its center of mass is moving with a constant velocityv_c_m on a horizontal ground . The rock gets dislodged and thrown in the air at a certain instance. Answer the following questions in terms of given variables and other fundamental constants as needed.

(a) Determine the angle at which the rock must be dislodged to reach the maximum height.

(b) Determine the maximum height.