Answer
The block's speed is $~1.99~m/s$
Work Step by Step
We can use energy and work to find the speed of the block:
$KE_f = U_0+Work$
$\frac{1}{2}mv^2 = mgh-mg~cos~\theta~\mu_k~d$
$\frac{1}{2}mv^2 = mgd~sin~\theta-mg~\mu_k~d~cos~\theta$
$v^2 = 2gd~(sin~\theta-\mu_k~cos~\theta)$
$v = \sqrt{2gd~(sin~\theta-\mu_k~cos~\theta)}$
$v = \sqrt{(2)(9.80~m/s^2)(0.30~m)~[sin~60.0^{\circ}-(0.38)~cos~60.0^{\circ}]}$
$v = 1.99~m/s$
The block's speed is $~1.99~m/s$.
