Home > Courses > 1P21_Sternin > Kinematics Kinematics in 2D Instantaneous velocity $\vec{V} = \lim_{\Delta t \rightarrow 0} \overline{\vec{V}}$ is tangential to the trajectory The principle of superposition: $x$--motion is independent of $y$--motion Projectile motion a special case of $a = \mbox{const} = -g$ time--of--flight, $t=\sqrt{2h/g}$ range, $R=V_0\sqrt{2h/g}$ velocity $\vec{V}$ at impact, $\left\{ \begin{array}{l} V=\sqrt{V_0^2+2gh} \\ \theta=\arctan ({-\sqrt{2gh}}/{V_0}) \end{array} \right.$ maximum range $R=\frac{V_0^2}{g} \> \sin(2\alpha) = \frac{V_0^2}{g} \quad \mbox{when} \quad \alpha=45^\circ$