Answer
x = 240 m
Work Step by Step
We can use a force equation to find the acceleration while the skier is on the incline:
$ma = \sum F$
$ma = mg ~sin(\theta) - mg ~cos(\theta)\cdot \mu_k$
$a = g ~sin(\theta) - g ~cos(\theta)\cdot \mu_k$
$a = (9.80 ~m/s^2) ~sin(28^{\circ}) - (9.80 ~m/s^2) ~cos(28^{\circ}) \cdot (0.18)$
$a = 3.04~m/s^2$
We can use kinematics to find the velocity $v$ at the bottom of the incline:
$v^2 = v_0^2 + 2ax$
$v = \sqrt{v_0^2 + 2ax}$
$v = \sqrt{(5.0 ~m/s)^2 + (2)(3.04 ~m/s^2)(110 ~m)}$
$v = 26.3 ~m/s$
We can use a force equation to find the rate of deceleration while the skier is on the flat surface:
$ma = \sum F$
$ma = mg ~ \mu_k$
$a = g ~ \mu_k$
$a = (9.80 ~m/s^2)(0.15)$
$a = 1.47~m/s^2$
We can use kinematics to find the distance $x$ that the skier travels along the flat surface. We can use $v_0 = 26.3 ~m/s$ for this part of the question:
$x = \frac{v^2 - v_0^2}{2a} = \frac{0 - (26.3 ~m/s)^2}{(2)(-1.47 ~m/s^2)} = 240 ~m$
