Answer
(a) The brick is moving with a speed of $4.43~m/s$
(b) The brick is moving with a speed of $4.03~m/s$
Work Step by Step
(a) We can use the conservation of energy to find the final speed of the brick:
$KE_2+U_2 = KE_1+U_1$
$KE_2 = 0+U_1-U_2$
$\frac{1}{2}mv^2 = -mg~\Delta h$
$v^2 = -2g \Delta h$
$v = \sqrt{-2g~\Delta h}$
$v = \sqrt{-(2)(9.80~m/s^2)(-2.00~m)~sin~30.0^{\circ}}$
$v = 4.43~m/s$
The brick is moving with a speed of $4.43~m/s$
(b) We can use work and energy to find the speed of the brick:
$KE_2+U_2 = KE_1+U_1+Work$
$KE_2 = 0+U_1-U_2+Work$
$\frac{1}{2}mv^2 = -mg~\Delta h-mg~cos~\theta~\mu_k~d$
$v^2 = 2gd~sin~\theta -2g~cos~\theta~\mu_k~d$
$v^2 = 2gd~(sin~\theta -cos~\theta~\mu_k)$
$v = \sqrt{2gd~(sin~\theta -cos~\theta~\mu_k)}$
$v = \sqrt{(2)(9.80~m/s^2)(2.00~m)~(sin~30.0^{\circ} -(0.10)~cos~30.0^{\circ})}$
$v = 4.03~m/s$
The brick is moving with a speed of $4.03~m/s$
