Answer
The speed after it has traveled 0.400 meters up the wall is 1.78 m/s.
Work Step by Step
We can use a force equation to find the acceleration.
$\sum F = ma$
$F~sin(\theta) - F~cos(\theta)~\mu_k - mg = ma$
$a = \frac{F~sin(\theta) - F~cos(\theta)~\mu_k - mg}{m}$
$a = \frac{(96.0~N)~sin(60.0^{\circ}) - (96.0~N)~cos(60.0^{\circ})(0.300) - (5.00~kg)(9.80~m/s^2)}{5.00~kg}$
$a = 3.95~m/s^2$
We can use the acceleration to find the speed $v$.
$v^2= v_0^2+2ay = 0 +2ay$
$v=\sqrt{2ay} = \sqrt{(2)(3.95~m/s^2)(0.400~m)}$
$v = 1.78~m/s$
The speed after it has traveled 0.400 meters up the wall is 1.78 m/s.
