$1.5.3$ A wedge has a slope's angle of 30$^\circ$. A vertical rod goes down with velocity $v$ and pushes the wedge. What velocity will develope the wedge?
Firstly, we suppose there is no any friction. For a better understanding of the problem, consider the following figure
According to figure $$\tan{30^\circ}=\frac{S_r}{S_w}$$ and this relation is valid for velocities too because the motion is uniform (at constant speed) $$\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$$ So, separating $v_w$ $$\boxed{v_w=v\sqrt{3}}$$
BSc. Luis Daniel Fernández Quintana
Physics Department (FCNE)
Universidad de Oriente, Cuba