We will have the following:
We are given the following:
![\begin{cases}m_{\text{ball}}=9\operatorname{kg} \\ m_(pin)=2\operatorname{kg} \\ v_(pin)=11.04m/s \\ v_{\text{ball}}=1.8m/s\end{cases}]()
So, we will have to proceed as follows:
First, we calculate the momentum of the pin:
![\tau_(pin)=(2\operatorname{kg})(11.04m/s)\Rightarrow\tau_(pin)=22.08\operatorname{kg}\cdot m/s]()
Now, we calculate the final momentum of the ball:
![\tau_{f\text{ball}}=(7\operatorname{kg})(1.8m/s^2)\Rightarrow\tau_{\text{fball}}=12.6\operatorname{kg}\cdot m/s]()
Now, we will have that the original momentum of the ball would be:
![\tau_{\text{iball}}=\tau_{\text{fball}}+\tau_(pin)\Rightarrow\tau_{\text{iball}}=12.6\operatorname{kg}\cdot m/s+22.08\operatorname{kg}\cdot m/s]()
![\Rightarrow\tau_{\text{iball}}=34.68\operatorname{kg}\cdot m/s]()
Now, we find it's initial speed:
![\tau_{\text{iball}}=m\cdot v_i\Rightarrow34.68\operatorname{kg}\cdot m/s=(7\operatorname{kg})\cdot v_i]()
So, the initial speed of the ball was of 867/175 m/s, that is approximately 4.95 m/s.