### Vector Geometry

Food for thought

A ball is thrown from a position $O$ on level ground with initial velocity (in $\mathrm{m\,s^{-1}}$) $\mathbf{u}=5\mathbf{i}+6\mathbf{j}$ where $\mathbf{i}$ is a horizontal direction and $\mathbf{j}$ is vertically upwards.
Taking gravity to be $\quantity{10}{m\,s^{-2}}$ and ignoring air resistance, find how far from $O$ the ball will land and find an equation for the trajectory of the ball.