A bowling ball of mass M and radius R is thrown such that at the instant it touches the floor it is moving horizontally with a speed v₀ and is not rotating. It slides for a time t₁ a distance s₁ before it begins to roll without slipping. 

(a) If μ_k is the coefficient of sliding friction between the ball and the floor, find s₁, t₁, and the final speed v₁ of the ball. 

(b) Find the ratio of the final mechanical energy to the initial mechanical energy of the ball. 

(c) Evaluate these quantities for v₀ = 8 m/s and μ_k = 0.06.