Physics - Center of Mass Question with Solution | TestHub

Let the x-axis be perpendicular to the wall and the y-axis be parallel to the wall. Initial velocity components: $v_x=-v\sin (30^{\circ })$ and $v_y=v\cos (30^{\circ })$. Final velocity components: $v_x^{\prime }=v\sin (30^{\circ })$ and $v_y^{\prime }=v\cos (30^{\circ })$. Impulse is the change in momentum: $\vec{J}=\Delta \vec{P}=m({\vec{v}}^{\prime }-\vec{v})$. Change in x-momentum: $\Delta P_x=m(v\sin (30^{\circ })-(-v\sin (30^{\circ })))=2mv\sin (30^{\circ })$. Change in y-momentum: $\Delta P_y=m(v\cos (30^{\circ })-v\cos (30^{\circ }))=0$. The magnitude of the impulse is $|\vec{J}|=\sqrt{(\Delta P_x{)}^2+(\Delta P_y{)}^2}=|2mv\sin (30^{\circ })|$. Since $\sin (30^{\circ })=1/2$, the magnitude of the impulse is $2mv(1/2)=mv$.