Physics - Center of Mass Question with Solution | TestHub

We have the following equations:

$2m{v}_x^{\prime }=mv\cos \theta -mv\cos \theta =0$

This implies $v_x^{\prime }=0$.

For the y-component, we have:

$$2m{v}_y^{\prime }=2mv\sin \theta$$

$$v_y^{\prime }=v\sin \theta$$

The initial kinetic energy is given by:

$$K_i=\frac{1}{2}(2m)(v^2{\cos }^2\theta )+\frac{1}{2}m{v}^2{\sin }^2\theta$$

The final kinetic energy is:

$$K_f=\frac{1}{2}(2m)v^2{\sin }^2\theta$$

The loss in kinetic energy is:

$$\Delta K_{Loss}=K_i-K_f=m{v}^2{\cos }^2\theta$$