Answer: a) 23 m/s
Explanation: In order to solve this problem we have to consider the circular movement where the friction force change de direcion of the velocty to keep a circular trajectory.
By using Second Newton law, we have:
F=m*acentripeta
μ*N= m*v^2/r where N ( equal to mg) is the normal force and μ is the coefficient of friction. r is the redius of the trajectory.
so
the maximun speed permited to keep a circular trajectory is calculated as:
v= (μ*r*g)^1/2=(0.65*80m*9.8 m/s^2)^1/2=22.57 m/s