(Solved): An astronaut in a maneuvering unit approaches a space station. At the present instant, the station ...

An astronaut in a maneuvering unit approaches a space station. At the present instant, the station informs him that his position relative to the origin of the station's coordinate system is \( \mathbf{r}_{G}=40 \mathbf{i}+70 \mathbf{j}+180 \mathbf{k}(\mathrm{m}) \) and his velocity is \( \mathbf{v}=4.7 \mathbf{j}+3 \mathbf{k}(\mathrm{m} / \mathrm{s}) \). The position of an airlock is \( \mathbf{r}_{A}=0 \mathbf{i}+30 \mathbf{k}(\mathrm{m}) \). Determine the angle between his velocity vector and the line from his position to the airlock's position. (Figure 1) Express your answer with the appropriate units.