Answer
t = 4.8 seconds
Work Step by Step
We can use a force equation to find the acceleration:
$\sum ~F = ma$
$mg ~sin(\theta) - mg ~cos(\theta)\cdot \mu_k = ma$
$a = g ~sin(\theta) - g ~cos(\theta)\cdot \mu_k$
$a = (9.80 ~m/s^2)\sin(8.0) - (9.80 ~m/s^2) ~cos(8.0)\cdot (0.060)$
$a = 0.78 ~m/s^2$
We can use the acceleration to find the time to slide down.
$x = \frac{1}{2}at^2$
$t = \sqrt{\frac{2x}{a}} = \sqrt{\frac{(2)(9.0 ~m)}{0.78 ~m/s^2}} = 4.8~s$
It takes 4.8 seconds for the bar of soap to slide down to the bottom of the ramp.
