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=(v_1sin\theta_1)/(sin\theta_2)=(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= (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

`(1)/(2)m(v^2_1+v^2_2)=(1)/(2)(1.37)(2.531^2+1.84^2)=6.07J`