Learning Goal: To practice Tactics Box 9.1 Drawing a before-and-after visual overview.

During a collision, two objects exert forces on each other that vary in a complex way during the time of the collision. Using Newton’s second law to predict the outcome of a collision would thus be a daunting challenge. Nevertheless, some collisions have very simple outcomes that can be predicted by analyzing the motion of the objects before and after the collision. A before-and-after visual overview is therefore an important problem-solving tool in such problems. The following Tactics Box explains how to draw a visual overview focusing on the connection between “before” and “after.”

A) Which of the following sketches best represents the situation before and after the collision? Vectors  and  represent, respectively, the velocities of the puck before and after the collision with the stick.

B) Draw the most appropriate x axis for this problem in the diagram below. The orientation of your vector will be graded. The location and length of the vector will not be graded.

C) To complete your visual overview of the problem, you should compile two lists: one of known quantities and one listing the unknown variables that will allow you to answer the question in the problem. Below are all of the relevant quantities in this problem: the initial and final velocities of the puck (v_x) and (v_x)_f, the magnitude J_x of the impulse delivered by the stick, and the mass m of the puck. Sort them accordingly.