Question

I'm having trouble solving 2-d momentum problems, I attached an example that I've been stuck on for some time.

Answer 1

4.27 m/s

Step-by-step explanation:

To find the x-component of the ball's final velocity we will use the conservation of momentum in the x-direction, so

`\begin{gathered} p_(ix)=p_(fx) \\ m_bv_(bi)=m_bv_(fb)+m_pv_(fp) \end{gathered}`

Where mb is the mass of the ball, Vbi is the initial velocity of the ball in x, Vfb is the final velocity of the ball in x, mp is the mass of the pin and Vfp is the final velocity of the pin in x. We can replace each value as

mb = 7.50 kg

Vbi = 6.42 m/s

Vfb = ?

mp = 1.60 kg

Vfp = (14.8 m/s)cos(-47) = 10.094 m/s

Then, we can solve the expression for Vfb

`\begin{gathered} m_bv_(bi)-m_pv_(fp)=m_bv_(fp) \\ v_(fp)=(m_bv_(bi)-m_pv_(fp))/(m_b) \end{gathered}`

Finally, replace the values to get

`\begin{gathered} v_(fp)=\frac{\left(7.5\right)\left(6.42\right)-\left(1.6\right)\left(10.094){}\right.}{7.5} \\ v_(fp)=4.27\text{ m/s} \end{gathered}`

Therefore, the x-component of the ball's final velocity is 4.27 m/s