Chapter 8 - Potential Energy and Conservation of Energy - Problems and Conceptual Exercises - Page 251: 97

$0.688m$

We know that $W_{nc}=E_f-E_i$ $W_{nc}=(K.E_f+U_f)-(K.E_i+U_i)$ $W_{nc}=(\frac{1}{2}mv_f^2+0)-(0+mgh)$ $\implies -\mu_k mgd=\frac{1}{2}mv_f^2-mgh$ This can be rearranged as: $mgh=m(\frac{1}{2}v_f^2+\mu_kgd)$ $\implies h=\frac{v_f^2}{2g}+\mu_kgd$ We plug in the known values to obtain: $h=\frac{(3.50)^2}{2(9.81)}+(0.640)(0.100)$ $h=0.688m$