let the friction coefficient on dry ice and wet ice is different and given as
[tex]\mu_d [/tex] = on dry ice
[tex]\mu_w [/tex] = on wet ice
now by friction force formula we can say
[tex]F_f = -\mu mg[/tex]
so the deceleration due to friction force is given as
[tex]a = -\mu g[/tex]
now the deceleration due to friction force on both surface is given as
[tex]a_1 = -\mu_d * g[/tex]
[tex]a_2 = -\mu_w * g[/tex]
now the time to stop the two blocks can be calculated by kinematics
[tex]v_f - v_i = a t[/tex]
[tex]0 - v_0 = -\mu_d * g * t_d[/tex]
[tex]t_d = \frac{v_0}{\mu_d* g}[/tex]
also for other block on wet ice we can say similarly
[tex]t_w = \frac{v_0}{\mu_w*g}[/tex]
now the ratio of two time on two surfaces is given as
[tex]\frac{t_d}{t_w} = \frac{\mu_w}{\mu_d}[/tex]
so this is the ratio of time on two surfaces
