Answer
The average coefficient of friction was 0.091.
Work Step by Step
The potential energy at the highest point on the slope is equal to the original kinetic energy plus the work done by friction. Therefore,
$KE + Work = PE$
$Work = PE - KE$
$F_f~d\times cos(180) = mgh -\frac{1}{2}mv^2$
$-mg\mu ~d = mgh -\frac{1}{2}mv^2$
$-\mu = \frac{gh -\frac{1}{2}v^2}{gd}$
$-\mu = \frac{(9.8 ~m/s^2)(15 ~m\times sin(19)) -\frac{1}{2}(11.0 ~m/s)^2}{(9.8 ~m/s^2)(cos(19))(15 ~m)}$
$\mu = 0.091$
The average coefficient of friction was 0.091.
