\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Impulse and Momentum Problems

• Start with the equation $$\vec p_f=\vec p_i + \vec J$$ where $\vec J$ is the total impulse on the object.
• If you are given either momentum or impulse directly, then fill it into the equation.
• If not, use $\vec p=m\vec v$ and $\vec J=F_{avg}\Delta t$.
• Fill in all the values that you are given, then solve for the value that you are asked for.
• If the problem is in two dimensions, you will have separate equations for horizontal and vertical components: think $$p_{fx} = p_{ix}+J_x \qquad \hbox{AND} \qquad p_{fy}=p_{iy}+J_y$$

• If you like, you can use a table like the one on the right. Note that mass $m$ and the duration $\Delta t$ of the collision appear multiple times.