Question

What is the final speed of ball B after collision?

Answer 1

Given:

Mass of ball A, mA = 1.3 kg

Initial Velocity of ball A, uA = 2 m/s to the right

Mass of ball B, mB = 0.9 kg

Initial velocity of ball B, uB = 0 m/s (at rest)

Final velocity of ball A, vA = 1.5 m/s

θA = 30 degrees above the horizontal

θB = 60 degrees below the horizontal.

Let's find the final speed of ball B, vB, after the collision.

This is an elastic collision.

Let's apply the Conservation of Momentum:

`m_Au_A+m_Bu_B=m_Av_Acos_A+m_Bv_Bcos_B`

Thus, we have:

`\begin{gathered} (1.3)(2)+(0.9)(0)=(1.3)(1.5)(cos30)+(0.9)v_B(cos60) \\ \\ 2.6+0=1.69+0.9v_Bcos60 \end{gathered}`

Now, we have:

`\begin{gathered} 0.9v_Bcos60=2.6-1.69 \\ \\ v_Bcos60=(0.91)/(0.9) \\ \\ v_Bcos60=1.01 \\ \\ v_B=(1.01)/(cos60) \\ \\ v_B=2.02\text{ m/s} \end{gathered}`

Therefore, the final speed of ball B after the collision is 2.02 m/s.

• AInitiER:

2.02 m/s