(II) Billiard ball A of mass $m_{\mathrm{A}}=0.120 \mathrm{kg}$ moving with speed $v_{\mathrm{A}}=2.80 \mathrm{m} / \mathrm{s}$ strikes ball $\mathrm{B}$ , initially at rest, of mass $m_{\mathrm{B}}=0.140 \mathrm{kg} .$ As a result of the collision, ball $\mathrm{A}$ is deflected off at an angle of $30.0^{\circ}$ with a speed $v_{\mathrm{A}}^{\prime}=2.10 \mathrm{m} / \mathrm{s}$ (a) Taking the $x$ axis to be the original direction of motion of ball $A,$ write down the equations expressing the conservation of momentum for the components in the $x$ and $y$ directions separately. (b) Solve these equations for the speed, $v_{\mathrm{B}}^{\prime},$ and angle, $\theta_{\mathrm{B}}^{\prime},$ of ball B. Do not assume the collision is elastic.