Question

A white billiard ball with mass mw = 1.37 kg is moving directly to the right with a speed of v = 3.14 m/s and collides elastically with a black billiard ball with the same mass mb = 1.37 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ? w=54.0 kg

Answer 1

That latest value for the Angle is in Grads, not in Kilograms.

Apply law of conservation of momentum along vertical direction.

$m_1v_1sin\theta_1-m_2v_2sin\theta_2=0$

$v_2=\frac{v_1sin\theta_1}{sin\theta_2}=\frac{sin54}{sin36}v_1 = 1.376v_1$

Apply law of conservation of momentum along the horizontal direction

$m_1u_1=m_1v_1cos\theta_1+m_2v_2cos\theta_2$

$u_1=v_1(cos\theta_1+1.376cos\theta_2)$

$u_1=v_1(cos(54)+1.376cos(36))$

$u_1=(1.7) v_1$

$v_1= \frac{3.14}{1.7}=1.84m/s$

The second ball velocity is $v_2 = (1.376)(1.84)=2.531m/s$

The magnitud of final total momentum is

$m(v_1+v_2)=(1.37)(2.531+1.84)=5.98kgm/s$

The magnitude of final energy is

$\frac{1}{2}m(v^2_1+v^2_2)=\frac{1}{2}(1.37)(2.531^2+1.84^2)=6.07J$