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
\[
R=\frac{V_0^2}{g} \> \sin(2\alpha) = \frac{V_0^2}{g} \quad \mbox{when} \quad \alpha=45^\circ
\]
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